lens & mirrors

8/10/2019 Lens & Mirrors

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http://astro1.panet.utoledo.edu/~ljc/serfau23.html

1 Telescopes1.2 Optical elementsIn order to understand how telescopes work, it is useful to outline the basicprinciples of curved lenses and mirrors. A surface which is the same shape as asmall portion of a sphere is called a spherical (or more correctly spheroidal) surface.Surfaces with this shape have a special optical property which makes them highlyvaluable: their ability to bring light to a focus. Actually, the focusing properties of aspheroidal surface are not perfect, as we shall see later, but the imperfection isoften more than compensated for by the purely practical consideration that aprecise spheroidal optical surface can be produced much more easily and henceat much lower cos t than a precise aspheroidal (non -spheroidal) optical surface.Three important focusing properties of spheroidal surfaces are described in thethree following statements. Unfortunately, neither of the first two statements isexactly true for any real optics, but they are extremely valuable approximations tothe truth and will greatly aid your ability to understand the layouts of opticalinstruments such as telescopes and spectrographs.

1. When parallel rays of light pass through a lens with convex spheroidalsurfaces, or reflect from the surface of a spheroidal concave mirror, theyare brought to a focus. The distance of the focal point from the lens (ormirror) is called the focal length , f . This is a single quantity thatcharacterises the optical performance of the lens or mirror in question.

2. Light rays passing through the centre of a lens do not deviate from theiroriginal path.

3. Light paths do not depend on the direction in which light is travelling. So,for example, since parallel rays of light are brought to a focus by a convexlens at a distance f from the lens, then rays of light emanating from a pointa distance f away from the lens will be converted into a parallel beam. Alens which is used in such a way is called a collimator , and the beam of

parallel light that is produced is said to be collimated .Broadly speaking there are two sorts of lenses and mirrors used in optical systems.Converging (convex) lenses and converging (concave) mirrors each cause parallelrays of light to come together at the focal point, or focus, of the lens or mirror( Figure 1 a and b). In contrast, diverging (concave) lenses and diverging (convex)mirrors each cause parallel rays of light to spread out as if emanating from the focalpoint situated at a distance of one focal length from the centre of the lens or mirrorconcerned ( Figure 1 c and d).
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Figure 1: (a) A convex lens will cause parallel rays of light to converge to the

focal point. (b) A concave mirror will cause parallel rays of light to converge tothe focal point. (c) A concave lens will cause parallel rays to diverge as if from

the focal point. (d) A convex mirror will cause parallel rays to diverge as if fromthe focal point. The reflecting surface of the mirror is shown by a thicker black

lineConverging lenses and mirrors used individually can each produce real images ofdistant objects, by which is meant an image that may be captured on a screen ordirectly on a detector such as photographic film. Real images are those imagesmade by the convergence of actual rays of light. However, when eyepiece lenses

are used with telescopes, the final image formed by the telescope is said to bea virtual image , since it is situated at a location from which rays of light appear toemanate (see Figure 2 and Figure 3 below). Such an image cannot be captureddirectly on a detector. However, eyepieces are always used in conjunction withanother lens namely the lens of the eye itself which converts the virtualimage produced by the telescope into a real image on the retina of the eye.Two addition al comments should be made relating to the term focal length.Firstly, a series of two or more lenses and/or mirrors can also bring parallel incidentlight rays to a focus, though obviously at a different point from that of any of theelements independently. The focal length of such a series of optical elements isdefined as the focal length of a single lens that would bring the same rays of light toa focus at the same angle of convergence. The effective focal length may thereforebe quite different from the actual distance between the optics and the focus. As we

shall see later, this allows long focal lengths to be compressed into short pathlengths.Secondly, it is sometimes common to quote the number that is obtained by dividingthe focal length of an optical assembly by the diameter of the bundle of parallel lightrays that is brought to a focus. In some optical systems, such as telescopes, thediameter of this bundle of light rays is the same as the diameter of the main opticalelement, though this is not always the case, particularly for most camera lenses.The number obtained by calculating this ratio is referred to as the f-number ,written f/# or F/# where # is the numerical value.

What is the f-number of a 200 mm diameter telescope with a focallength of 2400 mm?
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Optics

Objectives:

EXPLAIN the law of reflection DISTINGUISH between specular and diffuse reflection LOCATE the images formed by plane mirrors EXPLAIN how concave and convex mirrors form images DESCRIBE properties and uses of spherical mirrors DETERMINE the locations and sizes of spherical mirror images SOLVE problems involving refraction EXPLAIN total internal reflection EXPLAINE some optical effects caused by refraction DESCRIBE how real and virtual images are formed by single convex and concave

lenses

LOCATE images formed by lenses using ray tracing and equations EXPLAIN how chromatic aberration can be reduced DESCRIBE how the eye focuses light to form an image EXPLAIN nearsightedness and farsightedness and how eyeglass lenses correct these

defects DESCRIBE the optical systems in some common optical instruments

VOCAB:Specular reflection- parallel light rays are reflected in parallelDiffuse reflection- scattering of light off a rough surfacePlane mirror- a flat, smooth surface from which light is reflected by specular reflection

Object- source of light rays that are to be reflected off a mirrored surfaceImage- combination of image points fromed by reflected light raysVirtual image- type of image formed by diverging light raysConcave mirror- miror with edges bent towards the observerPrincipal axis- straight line perpendicular to the mirror that divides the mirror in halfFocal point- the point at which incident light rays parallel to the prinicpal axis convergeFocal length- position of the focal point with respect to the mirror along the principal axisReal image- type of image fromed by converging light raysMagnification- the ratio of image height to object height; how much larger or smaller theimage is than the objectConvex mirror- reflective surface with edges that bend away from the observerLens- piece of transparent material that is used to focus light into an imageConvex Lens- lens thicker at the center than the edgesConcave Lens- lens thinner at the center than at the edges

MirrorsMirror Equation: 1/f=1/d i+1/d o do= object distance, d i= image distance, f= focal length, c= center of curvaturehi= image height, h o= object heightMagnification Equation: m= h i/ho= -d i/do

Law of reflection: The angle that a reflected ray makes with the surface of the mirror is equal to the

angle that the incident ray makes with the surface of the mirror.

LLdohiM C

thre


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Ray tracing is a method for finding the location, size and magnification of a reflected image by drawingrays coming off of the object and tracing where and how they would reflect. Using scale drawings is theonly way to get accurate results.

Images can be either real or virtual. Real images are formed by converging light rays, or light rayscoming together, and will be located on the same side of the mirror as the object. Virtual images areformed when reflected light rays diverge, or move away from each other. As shown in the picture above,the diverging rays can be traced back behind the mirror to show where the virtual image is located.

3 TYPES OF MIRRORSPlane mirrors are simply flat, smooth surfaces that light reflects off of. All light rays falling on themirror simply follow the law of reflection, and are easy to trace. Plane mirror images are always virtual.

Concave mirrors are bent inward, meaning the edges are bent towards the observer. They have a centerof curvature, which means that if the mirror were cut from a whole sphere, this point would be at thevery center. This point lies on the principal axis, which is the line going through the center of the mirror.The focal point is one half of the distance of the center of curvature, Concave mirrors can produce both

real and virtual images.

co Bi

Ttr


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Convex mirrors are the exact opposite of concave mirrors. They are bent so that the edges of the mirrorface away from the observer. Like concave mirrors, they can produce real and virtual images dependingon abject location.

RULES FOR RAY TRACING TO FIND AN IMAGE1. Light rays coming in parallel to the principal axis will reflect out through the focal point.2. A ray coming in through the focal point will reflect oout parallel to the principal axis.3.Rays coming through the center of curvature will reflecet back on themselves.4. A ray coming in to the vertex (the point where the principal axis and mirror meet) above the principalaxis will reflect at an equal angle below the principal axis.

R mwn1

hthtthht

In the section on mirrors, I learned how light rays reflect off of simple, concave, and convexmirrors. I learned how an image of an object is produced, and that a real image, not just avirtual image can be produced and can be projected on a screen from a mirror. From this, Ihave a better idea of how a projectorworks. From my understanding of focal poins, Iunderstand how flashlights and a car's headlights produce a beam of light. The bulb isfocused at the focal point of the convex mirror behind it and because of this all light rayscoming off the bulb reflect out straight ahead. I also now know that security mirros areconvex because they shrink the image size down to allow for more of the room to be shown.It is clear to me now ho weyeglasses work as well. For a person who has trouble seeingthings far away, they are prescribed a lens that will diverge the light rays slightly, so that they

focus correctly on the back of the eye. For problems seeing things up close, a converginglense is prescribed.
http://en.wikipedia.org/wiki/Opticshttp://www.cyberphysics.co.uk/topics/medical/Eye/eye.htmlhttp://www.opticampus.com/cecourse.php?url=ray_tracing/http://www.opticampus.com/cecourse.php?url=ray_tracing/http://www.cyberphysics.co.uk/topics/medical/Eye/eye.htmlhttp://en.wikipedia.org/wiki/Optics


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Reflection and Refraction

If a ray of light could be observed approaching and reflecting off of a flat mirror,then the behavior of the light as it reflects would follow a predictable law known as

the law of reflection. The diagram illustrates the law of reflection.

In the diagram, the ray of light approaching the mirror is known as the incident ray(see diagram). The ray of light leaving the mirror is known as the reflected ray. Atthe point of incidence where the ray strikes the mirror, a line can be drawn

perpendicular to the surface of the mirror; this line is known as a normal line. Theangle between the incident ray and the normal is known as the angle of incidence,i. The angle between the reflected ray and the normal is known as the angle ofreflection, q r . The law of reflection states that when a ray of light reflects off asurface, the angle of incidence is equal to the angle of reflection, i = r .

Reflection off of smooth surfaces leads to a type of reflection known as specularreflection. Reflection off of rough surfaces such as clothing, paper, and the asphaltroadway leads to a type of reflection known as diffuse reflection. The diagram

below depicts two beams of light incident upon a rough and a smooth surface.

The velocity of light, c, in a vacuum is about 3x10 8 meters per second. In othermedia (glass, for example) the velocity is less. The ratio of c to the actual velocityis called the refractive index, n:


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since ,

e = electric permittivitym = magnetic permeabilityk e = dielectric constant (e/e o )k m = relative permeability (m/m o )

The color of the light and its frequency are the same in both media. Therefore, thewavelength must shorten by the same ratio as the velocity. You can think of this"slowing down" of light in a transparent medium if you picture the mediumcomposed of individual atoms or molecules that can interact with the passing light

by absorbing and re-emitting the light. This absorbed and re-emitted light is addedto the component passing through at c in such a way that the sum is continuallyslowed down with respect to c. This continuous slowing down is equivalent to a

phase velocity less than c.

You can think of it like this: The electrons in the glass are driven to oscillate by thelight's E-field. This causes the electrons to become dipoles themselves and they begin to re-radiate or scatter. However, only the wavelets in the forward directionare IN PHASE and interfere constructively. The others interfere destructively andcancel out.


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3 Basic Laws

Three fundamental laws describe how a wavefront of light interacts with a surfacethat forms the boundary between materials with different refractive indices e.g. air-glass interface where air has a refractive index of 1 and glass is typically 1.5.

1) Incident, reflected, and transmitted waves lie all in the same plane

2) Angle of incidence is equal to the angle of reflection

i = r

3) SNELL'S LAW :

ni sin(i) = n t sin(t)

Where n i is index of refraction of the medium 1 and n t is index of refraction ofmedium 2


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Snell's Law allows us to calculate the new direction of propagation when light passes through an interface between two materials with different indices ofrefraction. The angles are measured between the normal to the surface and the light

beam. Light passing from a material with a high index of refraction to a materialwith a low index of refraction bends away from the normal whereas light passingfrom material with a low to material with a high index of refraction bends towardthe normal.

Fresnel's Equations

While Snell's law and the law of reflection tell us something about the direction inwhich reflected and refracted light propagate, it does not say anything about howmuch light goes where. When light strikes the interface between two materials with

different indices of refraction, a fraction of the light is reflected (R) and a fractionis transmitted (T). The values of R and T may be calculated using Fresnel'sequations. It is important to realize that 1) the sum of reflected and transmittedlight must equal the total incident light (since these are fractions R + T = 1); and 2)the angle of polarization of the incident EM wave with respect to the plane of theincident material has an effect on the respective fractions of light that aretransmitted or reflected.

a) E-Field perpendicular to the plane of incidence


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r = amplitude reflection coefficient, ratio of reflected to incident electric fieldamplitudes.

t = amplitude transmission coefficient, ratio of transmitted to incident electric fieldamplitudes.

b) E-field parallel to the plane of incidence


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Given that,R = Reflectance (W/m2)T = Transmittance (W/m2)

When there is no absorption, R + T = 1, and

If i = 0, the incident plane becomes undefined and

Examples:

1. What percent of light is reflected at the interface of air (n = 1.0) to glass(n = 1.5) if the angle of incidence is 0?

Answer:


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This means that in a lens, which has 2 air-glass interfaces, transmission througheach interface = 96%. This means that the transmission through the lens even itabsolutely non-absorbing is (0.96)2 = 0.9216. In other words 7.84% of the light is

lost due to reflection. Note that this property is multiplicative.

2. What percent of light is transmitted from air (n = 1.0) to glass (n = 1.4) if theangle of incidence is 48. Assume that the light is unpolarized.

Answer :

The easiest way to approach this is to calculate the fraction of light that isreflected. Assuming no absorption, the remainder is transmitted into the secondmedium.

First start with calculating the angle of refracted light using Snell's law. Given thati = 48

We can thus calculate the reflection coefficients for parallel and perperdicularly polarized light using Fresnel equations.

Substituting this into:

Next we have to realize the light is unpolarized. Practically we can handle this in

terms of Fresnel's equations by assuming that there is equal quantities of paralleland perpendicularly polarized light and the simply take the average:


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Thus R = 4.02%with T = 1 - R it follows that: T = 1 - 0.0402 = 0.9598

An Application of Fresnel Equations

The Fresnel equations describe the effects of an incoming electromagnetic planewave on the interface between two media with different dielectric constants orindices of refraction.

From the different Fresnel equations we obtain,

Here, note that while R can never be zero, R// is zero when (i + t) = 90. As aresult, for E-field parallel to the plane of incidence, the reflectance vanishes andthe beam is completed transmitted. This is Brewster's Law (see figure).


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Another way to look at this is that for parallel polarized light, there is an angle ofincidence where the reflectivity = 0. This angle, known as the Brewster's angle can

be calculated by:

Lenses and Lens Systems

A lens is typically made up of an optically translucent material containing two ormore refracting surfaces, at least one of which is curved. Lenses may be used in an

optical system to modify a beam of light or to form an image of an object. Thereare a number of factors that need to be considered when characterizing a lens:

Diameter : The diameter of a lens is typically chosen based on the size of the beamand object that needs to be modified.

Radius of Curvature : R determines how curved the lens is and the direction of thecurvature. It also relates to the focal length of the lens (see lens equations section).

Focal length : Focal point is defined as the point at which parallel rays coming intothe lens converge. The distance between the center of the lens at this point is thefocal length f of the lens. This point may be on the opposite side of the lens as in a


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convex lens or the same side as in a concave lens.

Transmission range : Any given material will allow light of certain wavelengths to be transmitted while allowing others to be absorbed. The lens material is chosen

based on the wavelength of the light that is being modified. e.g. glass transmitswell from 400 to 2500 nm, however quartz needs to be used to transmit light in theUV while more exotic materials need to be used for transmission further in the IR(for example: sapphire, CaF2, etc.).

Aberrations : Aberrations are limitations in lens behavior that can be detrimentalto its performance. These include spherical aberrations, chromatic aberrations,coma, and astigmatism.

There are six kinds of lenses, divided in two main categories; a) the positive or

convex lenses and b) the negative or concave lenses. The convex lenses have incommon that they are thicker in the center than at the edge while the concavelenses are thinner in the center than at the edges:

R 1 > 0 R 1 = R 1 > 0R 2 < 0 R 2 < 0 R 2 > 0

R 1 < 0 R 1 = R 1 > 0R 2 > 0 R 2 > 0 R 2 > 0


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where,R 1 = Radius of Curvature of the first lens surface from the left)R 2 = Radius of Curvature of the second lens surface (from the left)

Since all rays issuing from a source point will arrive at the image point, any tworays will fix that point. There are three rays that are easiest to apply. Two of thesemake use of the fact that a ray passing through the focal point will emerge from thelens parallel to the optical axis and vice versa; the third is the undeviated raythrough the center of the lens. They are illustrated below for both positive andnegative lenses.

Basic Lens Equations

1) The focal length of a lens can be calculated by the Gaussian Lens Formula :


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where, f = focal length,o = object distance,i = image distance

2) Another useful lens equation is the Lensmaker's Formula ;

where n l = index of refraction of the lensn2 = index of refraction of the surrounding medium typically air)

R 1 = Radius of Curvature of the first lens surface from the left)R 2 = Radius of Curvature of the second lens surface (from the left)

3) Transverse Magnification (MT) is defined as the magnification of the image inthe direction perpendicular to the direction of propagation and is given as:

4) Longitudinal Magnification (ML) is defined as the magnification of the imagein the direction of propagation and is given as

5) The transverse magnification of a two-lens system that is separated by a distanced that is greater than the sum of their focal lengths is given by:

The magnification in such a two-lens system is simply the product of themagnifications from each element:

Based on the location of the object relative to the focal point the location, size andtype of image will vary for a positive or negative lens.


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Curved Mirrors behave similar to lenses except that the formation of the image isreversed, i.e. the concave mirror behaves like a convex lens and a convex mirror

behaves like a concave lens.

EXAMPLES:

1. Construct the rays to form the image for a positive lens given that the focallength of the lens is 2 m and an object (1.5 m high) is placed at a distance of 3.5 m

from the lens.


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Answer: Given,f = 2 mo = 3.5 m

h(object)

= 1.5 m(Hint: To construct the image, draw the three rays described earlier)

Given that,

Thus i = 4.67 m

The magnification is given as,

Therefore, an object 1.5 m high will be magnified 1.33 times to yield an image1.995 m high. This image is real, inverted and magnified.

2. Construct the rays to form the image for a lens with focal length -10 cm and anobject that is placed at a distance of 10 cm from the lens. What kind of image do

you get?

Answer :Given,


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o = 10 cmf = -10 cm, therefore it is a concave (negative) lens.

Draw rays to construct the image.

Therefore i = - 5 cm

The magnification is given as,

Thus the image is a virtual, erect, minified image located at f/2.


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Aberrations

The formulas developed earlier for image formation by spherical reflecting andrefracting surfaces are, of course, only approximately correct. In deriving those

formulas it was necessary to assume paraxial rays, rays both near to the optical axisand making small angles with it. However, in considering these lens situations willarise when these assumptions are no longer valid and aberrations are observed.

1. Spherical Aberrations Spherical aberrations occur due to the severe curvature of short focal length orsmaller lenses because rays incident on the outer regions of a lens bend more thanthe rays towards the center, causing the image to appear out of focus.

Spherical aberrations are corrected by: using a larger lens orienting the lens correctly

using the right type of lens

2. Coma Coma is an off-axis aberration that is nonsymmetrical about the optical axis. Thisarises from the dependence of transverse magnification on the ray height at thelens. Because of coma, an off-axis object point is imaged as a blurred shape thatresembles a comet with a head and a tail. This type of image can be minimized byappropriate selection of the diameter of the lens to be used.


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3. Astigmatism When an object point lies far away from the optical axis, the incident cone of rayswill strike the lens asymmetrically giving rise to astigmatism. If the rays incidenton the lens in the plane of the paper (tangential plane) has a given focal length,

then the rays in the plane that is obliquely angled with respect to the paper (sagittal plane) has a different focal length. Thus, for the incident conical bundle of rays, thecross-section of beam as it leaves the lens is initially circular and gradually

becomes elliptical until it meets in a line at the focal point that is tangential to the plane of the paper.

4. Field of Curvature In this type of aberration, a given planar object is imaged on a parabolic surfaceinstead of a plane as can be seen in the figure.

5. Distortion Distortion shows up as a variation in the transverse magnification for points of theobject away from the optical axis. In other words, distortion occurs becausedifferent areas of the lens have different focal lengths and different transversemagnifications.


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6. Chromatic Aberration Chromatic aberration occurs for incident rays that contain many wavelengths.Since the index of refraction varies with wavelength, the focal properties of asimple lens will vary as well. The refractive index is higher for blue light than redlight. Therefore, the focal length of a convex lens is shorter for blue light than redlight.

Chromatic aberration can be corrected for using an achromatic doublet. Anachromatic doublet consists of a convex and concave lens made of differentmaterials cemented together. By choosing materials with appropriate refractiveindices, you can create a doublet that will have the same focal length at twowavelengths. The two lenses correct for each other and a focal point is found

somewhere in the middle.


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Tissue Optics

The two fundamental tasks of the field of tissue optics are:

1) Find the light per unit area per unit time that reaches a target chromophore atsome position, r, in the tissue and determine how much of that light is absorbed.2) Determine the absorption and scattering properties of tissue.

In describing the optical properties and light propagation in tissues, light is treatedas photons. Photons in a turbid medium such as tissue can move randomly in alldirections and may be scattered (described by its scattering coefficient s [m-1]) orabsorbed (described by its absorption coefficient a [m-1]). These coefficientsalong with anisotropy (i.e. the direction in which a photon is scattered if it isscattered) and index of refraction are referred to as the optical properties of a

material.

First let's consider a slab of tissue. If photons are hitting the tissue several thingscan happen:

1) Some photons will reflect off the surface of the material (similar to whathappens to glass and other materials - Fresnel's equations hold for tissue as well)2) The majority of the photons will enter the tissue upon which the following canhappen:


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a) the photon is absorbed (and can be converted to heat, trigger a chemical reactionor cause fluorescence emission)b) the photon is scattered (bumps into a particle and changes direction butcontinues to exist)

c) nothing (some photons can make it through the entire slab without running intoanything, they are neither scattered nor absorbed and will emerge on the other side- these are called ballistic photons).

For now let's forget about scattering and consider absorption first.


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Mirrors & Lenses

23.1 Flat Mirrors (also called plane mirrors)

An object viewed using a flat mirrorappears to be located behind the mirror,

because to the observer the diverging raysfrom the source appear to come from

behind the mirror.

The images reflected in flat mirrors have the following properties:

The image distance q behind the mirror equals the objectdistance p from the mirror

The image height h equals the object height h so that thelateral

magnification

The image has an apparent left-right reversal

The image is virtual, not real!

Real Image where the light ray actually come to a focus you can actually seethe object projected on a screen placed at that location


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Where is the image formed? What is its height? Draw two rays: one hitting Vand the other passing through C:

.We give this location a special name &


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designation : the focal point

. With this designation we can re-writethe concave spherical mirror equation

as:

Note, however, that truly spherical mirrorsdo not bring all rays to focus at the samelocation!

Spherical Aberration this is the problemthe Hubble Space Telescope had when firstlaunched.

23.3 Convex Mirrors (diverging mirrors) and Sign Conventions

Is the entry for Image location q correct?


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Example: Problem #6 A spherical Christmas tree ornament is 6.00 cm in diameter. What is themagnification of an object placed 10.0 cm away from the ornament?

Example: Problem #11 A 2.00-cm-high object is placed 3.00 cm in front of a concave mirror. If the imageis 5.00 cm high and virtual, what is the focal length of the mirror?

Example: Problem #16 A convex spherical mirror with a radius of curvature of 10.0 cm produces a virtualimage one-third the size of the real object. Where is the object?


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23.5 Atmospheric Refraction (read)

23.6 Thin Lenses

Note: a convex-concave lenses is sometimesreferred to as a meniscus. It is the shape used

for most eyeglasses.

Using the same sign convention for thin lenses:


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Example: Problem #36

An objects distance from a converging lens is ten times the focal length. How faris the image from the focal point? Express the answer as a fraction of the focallength.

Multiple Lenses

This is more complicated, but straightforward if you follow these rules:

1. Do the first lens as if the others werent there.

2. Use the image formed by this lens as the object of the next lens

3. Repeat this process for all the lenses in the system

4. The total magnification is just the product of the individual magnifications of each lens.

See Example 23.9 of the book

Example: Problem #41

Two converging lenses, each of focal length 15.0 cm, are placed 40.0 cm apart,and an object is placed 30.0 cm in front of the first. Where is the final image

formed, and what is the magnification of the system?

Microscope : Object very close to F 0 makes a real inverted larger image. This imageis then viewed & magnified further using the eyepiece.


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Telescope: Object near infinity forms a real inverted smaller image near the focal point. Eyepiece is used to magnify this image.

The angular magnification (how much bigger it looks) is just . To get different magnifications, just change eyepieces!

Most large telescopes use a concave mirrorinstead of a lens to form the image.


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Physics Tools for optics - Find Focal Length of thin lens using R 1 and R 2 radii Use this simple tool to solve physics problem related to thin lenses. You can use this tool find focallength for thin lens by giving lens radii and index of refraction of the material this lens made of. Pleaseremember to use correct sign convention when you enter radii.

Sign convention of lens radii R 1 and R 2 The signs of the lens radii indicate whether the corresponding surfaces are convex (R > 0, bulgingoutwards from the lens) or concave (R < 0, depressed into the lens). If R is infinite, the surface is flat,or has zero curvature, and is said to be planar.

Type of lenses

Using lensmaker's equation for thin lens, we can find focal length for lens


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Wikipedia's best work pleasing to the eye

However, also according to the standards, the images are not : of a high resolution

The image is approximately 450x450, but I believe it still does qualify under being a featured

image because it is a diagram, and not a photo. It is also sharp, clear, and looks good.

What I want to be reviewed is: 1- is the resolution okay 2- is it considered wikipedia's bets work

or pleasuring to the eye .. and therefore, should it be nominated as a featured picture or not.

Author : Myself User:Eshcorp

Pages they appear in: Curved mirror , but more could be added.

Nominate and support . - Eshcorp 07:43, 19 August 2006 (UTC)

Comments:

People are going to want svg. Broken S egue 15:10, 19 August 2006 (UTC) I don't know if it could be done as svg.. at least not with the tools I use, is there a good

vector drawing tool other than Inkscape that might provide more functionality? --Eshcorp 16:14, 19 August 2006 (UTC)

One small mistake - "curvature" is misspelled. Also, I think showing multiple rays of light and

their reflections would be better. See, for comparison, DrBob's lens diagrams (in svg). --

Davepape 16:52, 19 August 2006 (UTC) I will fix the mistake and add examples. It may take a while though. - -Eshcorp 17:29, 19

August 2006 (UTC)

I've made an SVG version in Inkscape. I'm dabbling in things I know nothing about as usual,

so let me know if anything needs to be changed on it and I'll get it sorted. If you like that I'll

make a similar one for the concave mirror. Icey 21:44, 25 August 2006 (UTC)

Seconder:
http://en.wikipedia.org/wiki/User:Eshcorphttp://en.wikipedia.org/wiki/User:Eshcorphttp://en.wikipedia.org/wiki/User:Eshcorphttp://en.wikipedia.org/wiki/Curved_mirrorhttp://en.wikipedia.org/wiki/Curved_mirrorhttp://en.wikipedia.org/wiki/Curved_mirrorhttp://en.wikipedia.org/wiki/User:Eshcorphttp://en.wikipedia.org/wiki/User:Eshcorphttp://en.wikipedia.org/wiki/User:Eshcorphttp://en.wikipedia.org/wiki/User:BrokenSeguehttp://en.wikipedia.org/wiki/User:BrokenSeguehttp://en.wikipedia.org/wiki/User:BrokenSeguehttp://en.wikipedia.org/wiki/User:BrokenSeguehttp://en.wikipedia.org/wiki/User:BrokenSeguehttp://en.wikipedia.org/wiki/User:BrokenSeguehttp://en.wikipedia.org/wiki/User:Eshcorphttp://en.wikipedia.org/wiki/User:Eshcorphttp://en.wikipedia.org/wiki/User:DrBob/Figures#2006http://en.wikipedia.org/wiki/User:DrBob/Figures#2006http://en.wikipedia.org/wiki/User:DrBob/Figures#2006http://en.wikipedia.org/wiki/User:Davepapehttp://en.wikipedia.org/wiki/User:Davepapehttp://en.wikipedia.org/wiki/User:Eshcorphttp://en.wikipedia.org/wiki/User:Eshcorphttp://en.wikipedia.org/wiki/User:Eshcorphttp://en.wikipedia.org/wiki/User:Iceyhttp://en.wikipedia.org/wiki/User:Iceyhttp://en.wikipedia.org/wiki/User:Iceyhttp://en.wikipedia.org/wiki/User:Iceyhttp://en.wikipedia.org/wiki/User:Eshcorphttp://en.wikipedia.org/wiki/User:Davepapehttp://en.wikipedia.org/wiki/User:DrBob/Figures#2006http://en.wikipedia.org/wiki/User:Eshcorphttp://en.wikipedia.org/wiki/User:BrokenSeguehttp://en.wikipedia.org/wiki/User:BrokenSeguehttp://en.wikipedia.org/wiki/User:Eshcorphttp://en.wikipedia.org/wiki/Curved_mirrorhttp://en.wikipedia.org/wiki/User:Eshcorp


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15. Light

You might have seen a beam of sunlight when it enters a room through a narrow opening or ahole.You may have also seen beams of light from the headlamps of scooters, cars and enginesof trains [Fig.1(a)]. Similarly, a beam of light can be seen from a torch. Some of

Fig.1(a) Rail Engine


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Fig.1(b) Light HouseFig.1: Beam of light

you may have seen a beam of searchlight from a light house or from an airport tower [Fig.1(b)].

What do these experiences suggest?

15.1 LIGHT TRAVELS ALONG A STRAIGHT LINEBoojho recalls an activity he performed in Class VI. In that activity he looked


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(a)

(b) Fig.2 Looking at a candle through a straight and bent pipe


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Fig.3 Reflection of objects in water

at a lighted candle first through a straight pipe and then through a bent pipe (Fig. 2). Why was

Boojho not able to see the candle flame through a bent pipe?This activity showed that light travels along straight lines.How can we change the path of light? Do you know, what happens when light falls on apolished or a shiny surface?

15.2 REFLECTION OF LIGHTOne way to change the direction of light is to let it fall on a shiny surface. For example, ashining stainless steel plate or a shining steel spoon can change the direction of light. Thesurface of water can also act like a mirror and change the path of light. Have you ever seen thereflection of trees or buildings in water (Fig.3)?

Any polished or a shiny surface can act as a mirror. What happens when light falls on a mirror?You have learnt in Class VI that a mirror changes the direction of light that falls on it. This

change of direction by a mirror is called reflection of light. Can you recall the activity in whichyou got the light of a torch reflected from a mirror? Let us perform a similar activity.

Activity 15.1

Take a torch. Cover its glass with a chart paper which has three slits as shown in Fig.5.Spread a sheet of chart paper

Paheli remembers the story of the lion and the rabbit from the Panchtantra , in whichthe rabbit fooled the lion by showing him his reflection in water (Fig.4).


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Fig.4 Reflection of the lion in water


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Fig.5 Reflection of light from a mirror

on a smooth wooden board. Fix a plane mirror strip vertically on the chart paper(Fig.5). Now direct the beam of light on the mirror from the torch with slits. Place thetorch in such a way that its light is seen along the chart paper on the board. Now adjust

its position so that the light from the torch strikes the plane mirror at an angle (Fig.5).Does the mirror change the direction of light that falls on it? Now move the torchslightly to either side. Do you find any change in the direction of reflected light?Look into the mirror along the direction of the reflected light. Do you see the slits inthe mirror? This is the image of the slits.

Paheli wants to know, what makes things visible to us? Boojho thinks that objects are visible onlywhen light reflected from them reaches our eyes. Do you agree with him?This activity shows howlight gets reflected from a plane mirror.Let us play around with the images formed in mirrors and know a little more about them.

Activity 15.2

CAUTION

Never touch a lighted electric bulb connected to the mains. It may be very hot and yourhand may get burnt badly. Do not experiment with the electric supply from the mainsor a generator or an inverter. You may get an electric shock, which may be dangerous.Use only electric cells for all the activities suggested here.

Place a lighted candle in front of a plane mirror. Try to see the flame of the candle inthe mirror. It appears as if a similar candle is placed behind the mirror. The candle,which appears behind the mirror, is the image of the candle formed by themirror(Fig.6). The candle itself is the object .

Now move the candle to different positions in front of the mirror. Observe the image ineach case.


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Fig.6 Image of a candle in a plane mirror

Boojho noted in his notebook: Is it not surprising that my image is of the same size as me whetherthe mirror is small or large?

Was the image upright in each case? Did the flame appear on top of the candle as in theobject? Such an image is called erect. An image formed by a plane mirror is erect andof the same size as the object.

Now place a vertical screen behind the mirror. Try to obtain the image of the candle onthis screen. Can you get the image on the screen? Now place the screen in front of themirror. Can you get the image on the screen now? You will find that the image of thecandle cannot be obtained on the screen in either case.What about the distance of the image from mirror? Let us perform another activity.

Activity 15.3

Take a chess board. If a chess board is not available, draw on a chart paper 64 (88)squares of equal size. Draw a thick line in the middle of the paper. Fix a plane mirrorvertically on this line. Place any small object, such as a pencil sharpner, at the

boundary of the third square counting from the mirror (Fig.7). Note the position of theimage. Now shift the object to the boundary of the fourth square. Again note the

position of the image. Did you find any relation between the distance of the image fromthe mirror and that of the object in front of it?


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Fig.7 Locating image in a plane mirror

Paheli made a note in her notebook: In a plane mirror the image is formed behind the mirror. It iserect, of the same size and is at the same distance from the mirror as the object is in front of it.

You will find that the image is at the same distance behind the mirror as the object is infront of it. Now verify this by placing the object anywhere on the chart paper.

15.3 RIGHT OR LEFT!When you see your image in a plane mirror, is it exactly like you? Have you ever noticed thatthere is one interesting difference between you and your image in a mirror? Let us find out.

Activity 15.4

Stand in front of a plane mirror and look at your image. Raise your left hand. Whichhand does your image raise (Fig. 8)? Now touch your right ear. Which ear does your

hand touch in your image? Observe carefully. You will find that in the mirror theright appears left and the left appears right. Note that only sides ar einterchanged; the image does not appear upside down.

Now write down your name on a piece of paper and hold it in front of a plane mirror.How does it appear in the mirror?


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Fig.8 Left hand appears on the right side in the image


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Fig.10 Image from the outer side of a spoon

Now look at your image using the inner side of the spoon. This time you may find thatyour image is erect and larger in size. If you increase the distance of the spoon fromyour face, you may see your image inverted (Fig.11). You can also compare the image

of your pen or pencil instead of your face.

Fig.11 Image from the inner side of a spoon


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The curved shining surface of a spoon acts as a mirror. The most common example of acurved mirror is a spherical mirror.If the reflecting surface of a spherical mirror is concave, it is called a concave mirror. Ifthe reflecting surface is convex, then it is a convex mirror (Fig.12).

Fig.12 A Comcave and Convex mirror

Why are concave and convex mirrors called spherical mirrors?

Take a rubber ball and cut a portion of it with a knife or a hacksaw blade[Fig.13(a)]. (Be careful. Ask an elder person to help you in cutting the ball). Theinner surface of the cut ball is called concave and the outer surface is called convex(Fig.13(b)).

Fig.13 A spherical mirror is a part of a sphere

The inner surface of a spoon acts like a concave mirror, while its outer surface acts likea convex mirror.We know that the image of an object formed by a plane mirror cannot be obtained on ascreen. Let us investigate if it is also true for the image formed by a concave mirror.

Activity 15.6

CAUTION

You will conduct Activity 6 in the sunlight. Be careful, never look directly towards thesun or its image as it may damage your eyes. You may look at the image of the sunwhen it is thrown on a screen or a wall.


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Fig.14 A concave mirror forms a real image of the sun

Take a concave mirror. Hold it facing the sun. Try to get the light reflected by themirror on a sheet of paper. Adjust the distance of the paper until you get a sharp brightspot on it (Fig. 14). Hold the mirror and the sheet of paper steady for a few minutes.Does the paper start burning?This bright spot is, in fact, the image of the sun. Notice that this image is formed on a

screen. An image formed on a screen is called a real image. Recollect that in Activity2 the image formed by a plane mirror could not be obtained on a screen. Such an imageis called a virtual image.

Now let us try to obtain on the screen the image of a candle flame formed by a concavemirror.

Activity 15.7

Fix a concave mirror on a stand (any arrangement to keep the mirror steady would do)and place it on a table(Fig.15). Paste a piece of white paper on a cardboard sheet (sayabout


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Fig.15 Real images formed by a concave mirror

15cm x 10cm). This will act as a screen. Keep a lighted candle on the table at adistance of about 50 cm from the mirror. Try to obtain the image of the flame on thescreen. For this, move the screen till a sharp image of the flame is obtained. Make surethat, the screen does not


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Fig.16 Virtual image formed by a concave mirror

obstruct the light from the candle falling on the mirror. Is this image real or virtual? Isit of the same size as the flame?

Now move the candle towards the mirror and place it at different distances from it. Ineach case try to obtain the image on the screen. Record your observation in Table 1. Isit possible to obtain the image on the screen when the candle is too close to the mirror(Fig.16)?We see that the image formed by a concave mirror can be smaller or larger in size thanthe object. The image may also be real or virtual.Concave mirrors are used for many purposes. You might have seen doctors using

concave mirrors for examining eyes, ears, nose and throat. Concave mirrors are alsoused by dentists to see an enlarged image of the teeth (Fig.17). The reflectors oftorches,headlights of cars and scooters are concave in shape (Fig.18).


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Fig.17 A Dentist examining a patient

Boojho observed his image in the shiny surface of the bell on his new bicycle. Hefound that his image was erect and smaller in size. He wondered

Fig.18 Reflector of a torch

if the bell is also a kind of spherical mirror. Can you recognise the type of the mirror? Note that the reflecting surface of the bell is convex.

Activity 15.8

Repeat Activity 7 now with a convex mirror in place of a concave mirror (Fig.19).Record your observations in a Table similar to Table 1.Could you get a real image at any distance of the object from the convex


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Fig.19 Image formed by a convex mirror

Table 1 Image formed by a concave mirror for object placed at different distances from it

Distance of the object fromthe mirror

Smaller/larger than theobject

Character of the image

Inverted/erect

Real/virtual

50 cm ... ..

40 cm ... ...

30 cm

20 cm

10 cm ...

5 cm


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Fig.20 Convex mirror as a side view mirror

mirror? Did you get an image larger in size than the object?Can you now recognise the mirrors used as side mirrors in scooters? These are convex

mirrors. Convex mirrors can form images of objects spread over a large area. So, thesehelp the drivers to see the traffic behind them (Fig.20).

15.5 IMAGES FORMED BY LENSESYou might have seen a magnifying glass. It is used to read very small print (Fig.21).You might have also used it to observe the body parts of a cockroach or an earthworm.The magnifying glass is actually a type of a lens.Lenses are widely used in spectacles, telescopes and microscopes. Try to add a fewmore uses of lenses to this list.Get some lenses. Touch and feel them. Can you find some difference just by touching?Those lenses which feel thicker in the middle than at the edges are convex lenses[Fig.22(a)]. Those


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Fig.21 A magnifying glass

which feel thinner in the middle than at the edges are concave lenses [Fig.22(b)].

Notice that the lenses are transparent and light can pass through them.

Fig.22 A convex lens and concave lens

Let us play with lenses.

CAUTION

It is dangerous to look through a lens at the sun or a bright light. You should also becareful not to focus sunlight with a convex lens on any part of your body.

Activity 15.9

Take a convex lens or magnifying glass. Put it in the path of sunrays. Place a sheet of paper as shown (Fig.23). Adjust the distance between the lens and the paper till you geta bright spot on the paper. Hold the lens and the paper in this position for a few


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minutes. Does the paper begin to burn? Now replace the convex lens with a concave lens. Do you see a bright spot

Fig.23 Real image of the sun by a convex lens

on the paper this time, too? Why are you not getting a bright spot this time?We have seen in the case of mirrors that for different positions of the object the natureand size of the image change.Is it true for lenses also?Let us find out. .

Activity 15.10

Take a convex lens and fix it on a stand as you did with the concave mirror. Place it ona table. Place a lighted candle at a distance of about 50 cm from the lens [Fig.25 (a)].Try to obtain the image

A convex lens converges (bends inward) the light generally falling on it [Fig.24 (a)].Therefore, it is called a converging lens. On the other hand, a concave lens diverges(bends outward) the light and is called a diverging lens [Fig.24 (b)].

Fig.24 Diverging lens


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of the candle on a paper screen placed on the other side of the lens. You may have tomove the screen towards or away from the lens to get a sharp image of the flame. Whatkind of image did you get? Is it real or virtual?

Now vary the distance of the candle from the lens [Fig.25 (b)]. Try to obtain the imageof the candle flame every time on the paper screen by moving it. Record your

observations as you did in Activity 7 for the concave mirror.It means that we can see the image formed by a lense from the side opposite to that of the object.

(a)


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Fig.27 Image formed by a concave lens

Did you get in any position of the object an image which was erect and magnified(Fig.26). Could this image be obtained on a screen? Is the image real or virtual? This ishow a convex lens is used as a magnifying glass.In a similar fashion study the images formed by a concave lens. You will find that theimage formed by a concave lens is always virtual, erect and smaller in size than theobject (Fig.27).

15.6 SUNLIGHT WHITE OR COLOURED?Have you ever seen a rainbow in the sky? You might have noticed that it appears usually afterthe rain when the sun is low in the sky. The rainbow is seen as a large arc in the sky with manycolours (Fig.28).


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Fig.28 A rainbow

Fig.29 A CD placed in sun

How many colours are present in a rainbow? When observed carefully, there are seven coloursin a rainbow, though it may not be easy to distinguish all of them. These are red, orange,yellow, green, blue, indigo and violet.

Does this mean that the white light consists of seven colours? (a) A disc with seven colours (b) Itappears white on rotating

You might have seen that when you blow soap bubbles, they appear colourful. Similarly, whenlight is reflected from the surface of a Compact Disk (CD), you see many colours (Fig.29).

On the basis of these experiences, could we say that the sunlight is a mixture of differentcolours? Let us investigate.


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Activity 15.11

Take a glass prism. Allow a narrow beam of sunlight through a small hole in thewindow of a dark room to fall on one face of the prism. Let the light coming out of theother face of the prism fall on

Paheli wants to tell you that you can see a rainbow only when your back is towards the sun.

Fig.30 A prism splits sunlight into seven colours

a white sheet of paper or on a white wall. What do you observe? Do you see colourssimilar to those in a rainbow (Fig.30)? This shows that the sunlight consists of sevencolours. The sunlight is said to be white light. This means that the white light consistsof seven colours. Try to identify these colours and write their names in your notebook.Can we mix these colours to get white light? Let us try.

Activity 15.12

Take a circular cardboard disc of about 10 cm diameter. Divide this disc into sevensegments. Paint the seven rainbow colours on these segments as shown in Fig.31 (a).You can also paste, coloured papers on these segments. Make a small hole at the centreof the disc. Fix the disc loosely on the tip of a refill of a ball pen. Ensure that the discrotates freely [Fig.31 (a)]. Rotate the disc in the daylight. When the disc is rotated fast,the colours get mixed together and the disc appears to be whitish [Fig.31 (b)]. Such adisc is popularly known as Newtons disc.


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Fig.31 (a) A disc with seven colours (b) It appears white on rotating

Paheli has a brilliant idea! Shehas prepared a small top with a small circular disc withseven rainbow colours painted on it (Fig.32). When the top rotates it appears nearlywhite.

Fig.32 A top with seven colours

Keywords

Concave lens Concave mirror Convex lens

Convex mirror Erect image Magnified image


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Magnifying glass Prism Rainbow Real image Rear view mirror Side mirror

Spherical mirror Virtual image

What you have learnt

Light travels along straight lines. Any polished or a shining surface acts as a mirror. An image which can be obtained on a screen is called a real image. An image which cannot be obtained on a screen is called a virtual image. The image formed by a plane mirror is erect. It is virtual and is of the same size as the object.

The image is at the same distance behind the mirror as the object is in front of it.

In an image formed by a mirror, the left side of the object is seen on the right side in theimage, and right side of the object appears to be on the left side in the image. A concave mirror can form a real and inverted image. When the object is placed very close to

the mirror, the image formed is virtual, erect and magnified. Image formed by a convex mirror is erect, virtual and smaller in size than the object. A convex lens can forms real and inverted image. When the object is placed very close to the

lens, the image formed is virtual, erect and magnified. When used to see objects magnified,the convex lens is called a magnifying glass.

A concave lens always forms erect, virtual and smaller image than the object. White light is composed of seven colours.

E X E R C I S E

1. Fill in the blanks:

o An image that cannot be obtained on a screen is called

o Image formed by a convex is always virtual and smaller in size

o An image formed by a mirror is always of the same size as that of the object

o An image which can be obtained on a screen is called a image

o An image formed by a concave cannot be obtained on a screen.

2. Mark T if the statement is true and F if it is false:

S.No Option Ture/False

a.We can obtain an enlarged and erect image by a convexmirror.

True

False

b. A concave lens always form a virtual image.True

False


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Choose the correct option in questions 11 13

12. A virtual image larger than the object can be produced by a

S.No Option

a. concave lens

b. concave mirror

c. convex mirror

d. plane mirror

13. David is observing his image in a plane mirror. The distance between the mirror and his imageis 4 m. If he moves 1 m towards the mirror,then the distance between David and his imagewill be

S.No Option

a. 3 m

b. 5 m

c. 6 m

d. 8 m

14. The rear view mirror of a car is a plane mirror. A driver is reversing his car at a speed of 2 m/s.

The driver sees in his rear view mirror the image of a truck parked behind his car. The speedat which the image of the truck appears to approach the driver will be

S.No Option

a. 1 m/s

b. 2 m/s


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c. 4 m/s

d. 8 m/s

Extended Learning Activities and Projects

1. Play with a mirrorWrite your name with a sketch pen on a thin sheet of paper, polythene or glass. Read yourname on the sheet while standing in front of a plane mirror. Now look at your image in themirror.

2. A burning candle in waterTake a shoe box, open on one side. Place a small lighted candle in it. Place a clear glass sheet(roughly 25 cm x 25 cm) infront of this candle (Fig.33). Try to locate the image of the candlebehind

Fig.33 Candle burning in water

the glass sheet. Place a glass of water at its position. Ask your friends to look at the image ofthe candle through the sheet of glass. Ensure that candle is not visible to your friends. Yourfriends will be surprised to see the candle burning in water. Try to explain the reason.

3. Make a rainbowTry to make your own rainbow. You can try this project in the morning or in the evening.Stand with your back towards the sun. Take a hosepipe or a water pipe used in the garden.Make a fine spray in front of you. You can see different colours of rainbow in the spray.

4. Visit a laughing gallery in some science centre or a science park or a village mela. You will findsome large mirrors there. You can see your distorted and funny images in these mirrors. Tryto find out the kind of mirrors used there.


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5. Visit a nearby hospital. You can also visit the clinic of an ENT specialist, or a dentist.Requestthe doctor to show you the mirrors used for examining ear, nose, throat and teeth. Can yourecognise the kind of mirror used in these instruments?

6. Role playHere is a game that a group of children can play. One child will be chosen to act as object and

another will act as the image of the object. The object and the image will sit opposite to eachother. The object will make movements, such as raising a hand, touching an ear, etc. Theimage will have to make the correct movement following the movement of the object. Therest of the group will watch the movements of the image. If the image fails to make thecorrect movement, she/he will be retired. Another child will take her/his place and the gamewill continue. A scoring scheme can be introduced. The group that scores the maximum willbe declared the winner.

Did You Know?

The mirrors can be used as weapons. Archimedes, a Greek scientist, is said to havedone just that more than two thousand years ago. When the Romans attacked Syracuse,a coastal city-state in Greece, Archimedes used mirrors arranged as shown in Fig. 34.The mirrors could be moved in any direction. They were positioned such that theyreflected the sunlight on the Roman soldiers. The soldiers were dazzled by the sunlight.They did not know what was happening. They got confused and ran away. This was anexample of triumph of ideas over military might.

Fig.34 Archimedes mirrors


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A biconvex lens.

Lenses can be used to focus light.


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A lens is a transmissive optical device which affects the focusing of a light

beam through refraction . A simple lens consists of a single piece of material, while a compound

lens consists of several simple lenses ( elements ), usually along a common axis. Lenses are

made from transparent materials such as glass , ground and polished to a desired shape. A lens

can be used to focus light to form an image , unlike a prism which refracts light without focusing.Devices which similarly refract radiation other than visible light are also called lenses, such

as microwave lenses or acoustic lenses.

The variant spelling lense is sometimes seen. While it is listed as an alternative spelling in some

dictionaries, most mainstream dictionaries do not list it as acceptable . [1][2]

History [edit ] This section

requires expansion with: historyafter 1758. (January 2012)

See also: History of optics and Camera lens

The Nimrud lens

The word lens comes from the Latin name of the lentil , because a double-convex lens is lentil-

shaped. The genus of the lentil plant i s Lens , and the most commonly eaten species is Lens

culinaris . The lentil plant also gives its name to a geometric figure .

The oldest lens artifact is the Nimrud lens , dating back 2700 years to ancient Assyria .[3][4] David

Brewster proposed that it may have been used as a magnifying glass , or as a burning-glass to

start fires by concentrating sunlight .[3][5] Another early reference to magnification dates back

to ancient Egyptian hieroglyphs in the 8th century BC, which depict "simple glass meniscal

lenses" .[6][verification needed ]

The earliest written records of lenses date to Ancient Greece , with Aristophanes ' play The

Clouds (424 BC) mentioning a burning-glass ( a biconvex lens used to focus the sun 's rays to

produce fire). Some scholars argue that the archeological evidence indicates that there was

widespread use of lenses in antiquity, spanning several millennia . [7] Such lenses were used by

artisans for fine work, and for authenticating seal impressions. The writings of Pliny theElder (23 79) show that burning-glasses were known to the Roman Empire ,[8]and mentions what
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g/wiki/Sunhttp://en.wikipedia.org/wiki/Sunhttp://en.wikipedia.org/wiki/Lens_(optics)#cite_note-7http://en.wikipedia.org/wiki/Lens_(optics)#cite_note-7http://en.wikipedia.org/wiki/Lens_(optics)#cite_note-7http://en.wikipedia.org/wiki/Seal_(emblem)http://en.wikipedia.org/wiki/Seal_(emblem)http://en.wikipedia.org/wiki/Seal_(emblem)http://en.wikipedia.org/wiki/Pliny_the_Elderhttp://en.wikipedia.org/wiki/Pliny_the_Elderhttp://en.wikipedia.org/wiki/Pliny_the_Elderhttp://en.wikipedia.org/wiki/Pliny_the_Elderhttp://en.wikipedia.org/wiki/Roman_Empirehttp://en.wikipedia.org/wiki/Roman_Empirehttp://en.wikipedia.org/wiki/Lens_(optics)#cite_note-8http://en.wikipedia.org/wiki/Lens_(optics)#cite_note-8http://en.wikipedia.org/wiki/File:Nimrud_lens_British_Museum.jpghttp://en.wikipedia.org/wiki/File:Wiki_letter_w_cropped.svghttp://en.wikipedia.org/wiki/File:Nimrud_lens_British_Museum.jpghttp://en.wikipedia.org/wiki/File:Wiki_letter_w_cropped.svghttp://en.wikipedia.org/wiki/Lens_(optics)#cite_note-8http://en.wikipedia.org/wiki/Roman_Empirehttp://en.wikipedia.org/wiki/Pliny_the_Elderhttp://en.wikipedia.org/wiki/Pliny_the_Elderhttp://en.wikipedia.org/wiki/Seal_(emblem)http://en.wikipedia.org/wiki/Lens_(optics)#cite_note-7http://en.wikipedia.org/wiki/Sunhttp://en.wikipedia.org/wiki/Focus_(optics)http://en.wikipedia.org/wiki/Lens_(optics)#Types_of_simple_lenseshttp://en.wikipedia.org/wiki/The_Cloudshttp://en.wikipedia.org/wiki/The_Cloudshttp://en.wikipedia.org/wiki/Aristophaneshttp://en.wikipedia.org/wiki/History_of_Ancient_Greecehttp://en.wikipedia.org/wiki/Wikipedia:Verifiabilityhttp://en.wikipedia.org/wiki/Lens_(optics)#cite_note-Kriss-6http://en.wikipedia.org/wiki/Egyptian_hieroglyphshttp://en.wikipedia.org/wiki/Ancient_Egypthttp://en.wikipedia.org/wiki/Magnificationhttp://en.wikipedia.org/wiki/Lens_(optics)#cite_note-Nimrud_lens-3http://en.wikipedia.org/wiki/Lens_(optics)#cite_note-Nimrud_lens-3http://en.wikipedia.org/wiki/Burning-glasshttp://en.wikipedia.org/wiki/Magnifying_glasshttp://en.wikipedia.org/wiki/David_Brewsterhttp://en.wikipedia.org/wiki/David_Brewsterhttp://en.wikipedia.org/wiki/Lens_(optics)#cite_note-Nimrud_lens-3http://en.wikipedia.org/wiki/Lens_(optics)#cite_note-Nimrud_lens-3http://en.wikipedia.org/wiki/Assyriahttp://en.wikipedia.org/wiki/Nimrud_lenshttp://en.wikipedia.org/wiki/Lens_(geometry)http://en.wikipedia.org/wiki/Lens_(genus)http://en.wikipedia.org/wiki/Lentilhttp://en.wikipedia.org/wiki/Nimrud_lenshttp://en.wikipedia.org/wiki/Camera_lenshttp://en.wikipedia.org/wiki/History_of_opticshttp://en.wikipedia.org/w/index.php?title=Lens_(optics)&action=edithttp://en.wikipedia.org/w/index.php?title=Lens_(optics)&action=edit&section=1http://en.wikipedia.org/wiki/Lens_(optics)#cite_note-1http://en.wikipedia.org/wiki/Lens_(optics)#cite_note-1http://en.wikipedia.org/wiki/Microwavehttp://en.wikipedia.org/wiki/Prismhttp://en.wikipedia.org/wiki/Imagehttp://en.wikipedia.org/wiki/Glasshttp://en.wikipedia.org/wiki/Transparency_(optics)http://en.wikipedia.org/wiki/Lens_(optics)#Compound_lenseshttp://en.wikipedia.org/wiki/Lens_(optics)#Compound_lenseshttp://en.wikipedia.org/wiki/Simple_lenshttp://en.wikipedia.org/wiki/Refractionhttp://en.wikipedia.org/wiki/Light_beamhttp://en.wikipedia.org/wiki/Light_beamhttp://en.wikipedia.org/wiki/Optics


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is arguably the earliest written reference to a corrective lens : Nero was said to watch

the gladiatorial games using an emerald (presumably concave to correct for nearsightedness ,

though the reference is vague) .[9] Both Pliny and Seneca the Younger (3 BC 65) described the

magnifying effect of a glass globe filled with water .

Excavations at the Viking harbour town of Frjel , Gotland , Sweden discovered in 1999 the rock

crystal Visby lenses , produced by turning on pole lathes at Frjel in the 11th to 12th century, with

an imaging quality comparable to that of 1950s aspheric lenses . The Viking lenses were capable

of concentrating enough sunlight to ignite fires . [10]

Between the 11th and 13th century "reading stones " were invented. Often used by monks to

assist in illuminating manuscripts, these were primitive plano-convex lenses initially made by

cutting a glass sphere in half. As the stones were experimented with, it was slowly understood

that shallower lenses magnified more effectively.

Lenses came into widespread use in Europe with the invention of spectacles , probably in Italy in

the 1280s .[11] This was the start of the optical industry of grinding and polishing lenses for

spectacles, first in Venice and Florence in the thirteenth century ,[12] and later in the spectacle-

making centres in both the Netherlands and Germany .[13] Spectacle makers created improved

types of lenses for the correction of vision based more on empirical knowledge gained from

observing the effects of the lenses (probably without the knowledge of the rudimentary optical

theory of the day) .[14][15] The practical development and experimentation with lenses led to the

invention of the compound optical microscope around 1595, and the refracting telescope in 1608,

both of which appeared in the spectacle-making centres in the Netherlands .[16][17]

With the invention of the telescope and microscope there was a great deal of experimentation

with lens shapes in the 17th and early 18th centuries trying to correct chromatic errors seen in

lenses. Opticians tried to construct lenses of varying forms of curvature, wrongly assuming errors

arose from defects in the spherical figure of their surfaces . [18]Optical theory on refraction and

experimentation was showing no single-element lens could bring all colours to a focus. This led

to the invention of the compound achromatic lens by Chester Moore Hall in England in 1733, an

invention also claimed by fellow Englishman John Dollond in a 1758 patent.

Construction of simple lenses [edit ] Most lenses are spherical lenses : their two surfaces are parts of the surfaces of spheres. Each

surface can be convex (bulging outwards from the lens), concave (depressed into the lens),

or planar (flat). The line joining the centres of the spheres making up the lens surfaces is called

the axis of the lens. Typically the lens axis passes through the physical centre of the lens,

because of the way they are manufactured. Lenses may be cut or ground after manufacturing to

give them a different shape or size. The lens axis may then not pass through the physical centre

of the lens.

Toric or sphero-cylindrical lenses have surfaces with two different radii of curvature in twoorthogonal planes. They have a different focal power in different meridians. This forms
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ikipedia.org/w/index.php?title=Lens_(optics)&action=edit&section=2http://en.wikipedia.org/w/index.php?title=Lens_(optics)&action=edit&section=2http://en.wiktionary.org/wiki/convexhttp://en.wiktionary.org/wiki/convexhttp://en.wiktionary.org/wiki/convexhttp://en.wiktionary.org/wiki/concavehttp://en.wiktionary.org/wiki/concavehttp://en.wiktionary.org/wiki/concavehttp://en.wikipedia.org/wiki/Toric_lenshttp://en.wikipedia.org/wiki/Toric_lenshttp://en.wikipedia.org/wiki/Focal_powerhttp://en.wikipedia.org/wiki/Focal_powerhttp://en.wikipedia.org/wiki/Focal_powerhttp://en.wikipedia.org/wiki/Focal_powerhttp://en.wikipedia.org/wiki/Toric_lenshttp://en.wiktionary.org/wiki/concavehttp://en.wiktionary.org/wiki/convexhttp://en.wikipedia.org/w/index.php?title=Lens_(optics)&action=edit&section=2http://en.wikipedia.org/wiki/John_Dollondhttp://en.wikipedia.org/wiki/Englandhttp://en.wikipedia.org/wiki/Chester_Moore_Hallhttp://en.wikipedia.org/wiki/Achromatic_lenshttp://en.wikipedia.org/wiki/Refractionhttp://en.wikipedia.org/wiki/Lens_(optics)#cite_note-18http://en.wikipedia.org/wiki/Lens_(optics)#cite_note-16http://en.wikipedia.org/wiki/Lens_(optics)#cite_note-16http://en.wikipedia.org/wiki/Netherlandshttp://en.wikipedia.org/wiki/Refracting_telescopehttp://en.wikipedia.org/wiki/Optical_microscopehttp://en.wikipedia.org/wiki/Lens_(optics)#cite_note-14http://en.wikipedia.org/wiki/Lens_(optics)#cite_note-14http://en.wikipedia.org/wiki/Lens_(optics)#cite_note-13http://en.wikipedia.org/wiki/Netherlandshttp://en.wikipedia.org/wiki/Lens_(optics)#cite_note-12http://en.wikipedia.org/wiki/Lens_(optics)#cite_note-11http://en.wikipedia.org/wiki/Italyhttp://en.wikipedia.org/wiki/Spectacleshttp://en.wikipedia.org/wiki/Magnificationhttp://en.wikipedia.org/wiki/Plano-convex_lenshttp://en.wikipedia.org/wiki/Illuminated_manuscripthttp://en.wikipedia.org/wiki/Monkhttp://en.wikipedia.org/wiki/Reading_stonehttp://en.wikipedia.org/wiki/Lens_(optics)#cite_note-10http://en.wikipedia.org/wiki/Aspheric_lenshttp://en.wikipedia.org/wiki/Pole_lathehttp://en.wikipedia.org/wiki/Visby_lenseshttp://en.wikipedia.org/wiki/Swedenhttp://en.wikipedia.org/wiki/Gotlandhttp://en.wikipedia.org/wiki/Fr%C3%B6jelhttp://en.wikipedia.org/wiki/Vikinghttp://en.wikipedia.org/wiki/Waterhttp://en.wikipedia.org/wiki/Seneca_the_Youngerhttp://en.wikipedia.org/wiki/Lens_(optics)#cite_note-9http://en.wikipedia.org/wiki/Myopiahttp://en.wiktionary.org/wiki/concavehttp://en.wikipedia.org/wiki/Emeraldhttp://en.wikipedia.org/wiki/Gladiatorhttp://en.wikipedia.org/wiki/Nerohttp://en.wikipedia.org/wiki/Corrective_lens


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an astigmatic lens. An example is eyeglass lenses that are used used to correct astigmatism in

someone's eye .

More complex are aspheric lenses . These are lenses where one or both surfaces have a shape

that is neither spherical nor cylindrical. The more complicated shapes allow such lenses to form

images with less aberration than standard simple lenses, but they are more difficult and

expensive to produce.

Types of simple lenses [edit ]

Lenses are classified by the curvature of the two optical surfaces. A lens is biconvex (or double

convex , or just convex ) if both surfaces are convex . If both surfaces have the same radius of

curvature, the lens is equiconvex . A lens with two concave surfaces is biconcave (or

just concave ). If one of the surfaces is flat, the lens is plano-convex or plano-concave depending

on the curvature of the other surface. A lens with one convex and one concave side is convex-concave or meniscus . It is this type of lens that is most commonly used in corrective lenses .

If the lens is biconvex or plano-convex, a collimated beam of light passing through the lens will

be converged (or focused ) to a spot behind the lens. In this case, the lens is called

a positive or converging lens. The distance from the lens to the spot is the focal length of the lens,

which is commonly abbreviated f in diagrams and equations.
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lens & mirrors

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