optics is the study of the nature and behavior of light

8/12/2019 Optics is the Study of the Nature and Behavior of Light

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Optics is the study of the nature and behavior of light.

It can be divided into subdisciplines based on the type of model used to describe light.

In physical optics, light is assumed to behave like a classical wave.

In quantum optics, light is assumed to have both wave and particle properties.

o Particles of light are called photons. In geometric optics, light is assumed to travel in a definite direction with relatively

little diffraction.

o This behavior is known as rectilinear propagation.

o The path of propagation of a light wave is a geometric ray.

The rays of geometric optics…

are perpendicular to the wave fronts of physical optics.

indicate the most probable path of the photons of quantum

optics.

A ray is the path of least action connecting two points in space and is

also…

the path of least time (the quickest path)

the path of least distance (the shortest path)

unique and therefore reversible

The principle of reversibility states that light will follow

exactly the same path if its direction of travel is

reversed.

Rays are…

straight lines in empty euclidean space

geodesics in general relativistic space-time

The eye can see something only if a ray from the object reaches the

eye.

Interface

An interface is the boundary between…

o two different media.

o two regions of a medium with different characteristics such as …

density (which is often related to temperature)

concentration of solute (salinity, for example)

mechanical stress

When an incident ray meets an interface it will be partially

o reflected

Reflected rays obey the law of reflection described in this section ofthis book.

o transmitted

Transmitted rays obey Snell's law, which is described in the next

section of this book.

o absorbed

Absorbed rays obey the law of conservation of energy. (The energy of

the ray is not destroyed, but changes form.)

http://physics.info/general-relativity/



http://physics.info/reflection/



http://physics.info/refraction/










Angles in geometric optics are measured with respect to a line normal to the

interface.

o The angle of incidence is the angle between the incident ray and the normal.

o The angle of reflection is the angle between the reflected ray and the normal.

o The angle of refraction is the angle between the transmitted ray and the

normal.

Reflection

Law of reflection: The angle of incidence equals the angle of reflection.

o The law of reflection can be derived from the principle of least action

The index of refraction.

n =c

v

where

n = index of refraction

c = speed of light in a vacuum

v = speed of light in a medium

The index of refraction is somewhat related to density, as one would expect. This graph is for

transparent minerals. Someone should make one for liquids and see what happens.

[slide]

Index of refraction for selected materials (λ ~ 590 nm)

material index material index

acetone 1.36 helium (gas) 1.000036

air ( – 15℃) 1.00030942 helium (liquid) ??

air ( 0℃) 1.00029238 hydrogen (gas) 1.000140

air (+15℃) 1.00027712 hydrogen (liquid) 1.0974

air (+30℃) 1.00026337 lucite 1.495

air (+60℃) 1.00023958 milk 1.35

alcohol, ethyl (grain) 1.361 oil, microscope 1.515

alcohol, methyl (wood) 1.328 oil, vegetable (50℃) 1.47

amber 1.546 opticon (epoxy) 1.545

amethyst 1.544 perovskite 2.38

benzene 1.501 plexiglas 1.488

http://physics.info/refraction/optical-density.html






butter (40℃) 1.455 quartz, crystalline 1.544

butter (60℃) 1.447 quartz, fused silica 1.4585

calcite 1.486 ruby 1.76

cd/dvd 1.55 salt 1.516

cocoa butter (40℃

) 1.457 sapphire 1.76diamond 2.418 sphalerite 2.428

eglestonite 2.49 topaz 1.62

emerald 1.576 turpentine 1.472

emerald, synth flux 1.561 ulexite 1.49

emerald, synth hydro 1.568 vacuum 1 exactly

eye, cornea 1.38 water (ice) 1.309

eye, aqueous humor 1.33 water (liquid, 0℃) 1.33346

eye, lens cover 1.38 water (liquid, 20℃) 1.33283

eye, lens 1.41 water (liquid, 100℃

) 1.31766eye, vitreous humor 1.34 water (vapor) 1.000261

fluorite 1.387 zircon, high 1.960

franklinite 2.36 zircon, low 1.920

glass, borosilicate (pyrex) 1.474 zirconia, cubic 2.173

glass, crown (soda-lime) 1.512

glass, fiber 1.560

glass, flint (29% lead) 1.569



glass, fused silica 1.4585

glycerin 1.473

apparent depth

Don't go in the water.

total internal reflection

light traveling from a slow medium to a fast medium

critical angle

n1 sin θ1 = n2 sin θ2

n1 sin θc = n2 sin 90°



sin θc =n2

in generaln1

sin θc =1

when the second media is airn1

inferior mirage

An inferior mirage.

It is sometimes possible to see over the horizon. The superior mirage or Fata Morgana.

"Fata Morgana (superior mirage), the Italian name of the enchanted, half sister of KingArthur. Italian writers and poets described these effects as seen over the straights of

Messina, between Italy and Sicily. Although the effects occur worldwide, the Italian

name sticks. (From Greenler's book?)"

Quote from somebody, "Under highly stable atmospheric conditions (typically on calm,clear nights), the radar beam can be refracted almost directly into the ground at some

distance from the radar, resulting in an area of intense-looking echoes. This "anomalous

propagation" phenomenon (commonly known as AP) is much less common than groundclutter. Certain sites situated at low elevations on coastlines regularly detect "sea return",

a phenomenon similar to ground clutter except that the echoes come from ocean waves."

dispersion

rainbow



A double rainbow seen on a depressingly gray

day in Clinton, Missouri.

You don't need rain for a rainbow. This picture

was taken at Niagara Falls, New York.

halo

A simple halo around a church in

Milwaukee, Wisconsin.

A 22° halo with an upper tangent arc and two sun dogs

as seen in New York City. The sun is blocked by theauthor's bicycle gloved fist.

Dispersion is generally highest in solids and lowest in gases.

Dispersion is often measured in terms of the coefficient of dispersion, which is defined as thedifference between the refractive indices for for two prominent lines in the spectrum of hydrogen

— the blue F line at 486.1 nm and the red C line at 656.3 nm.

n f − nc

Another common measure of dispersion is the dispersive power.

n f − nc

n D − 1

where nD is the index of refraction for the yellow D line of sodium at 589.0 nm.

Use of a single number to quantify dispersion is rather misleading. Index and wavelength are notlinearly related. Dispersion is best quantified as the rate of change of index of refraction with

wavelength.

dn

d λ

For most transparent materials, a graph of index versus wavelength is curve with a few generalcharacteristics.



The index of refraction is larger for shorter wavelengths; thus, its slope is always

negative.

Dispersion (the rate of change of index with wavelength) is greater for shorterwavelengths; thus, the graph starts out steep and gradually levels off.

birefringence

Calcite is a common, transparent mineral. It can be found throughout the world, but some of the

best samples were originally found in Iceland. Pieces of this mineral are easily split (or cleaved

as the geologists say) into parallelogram-faced prismatic chunks. Nonmetallic minerals thatcleave easily were called spar in German and so calcite is sometimes also known as Iceland spar.

It is of little economic importance by itself (although it is a component of limestone, which is

used to make cement), but is of some scientific importance. It has been known for several

centuries that light transmitted through calcite takes two paths. This can best be seen by laying alarge crystal of it on a page of text. Every letter can be seen twice. This phenomena is known as

double refraction or birefringence.



Double Refraction Through a Piece of Calcite

A ray of light incident on a doubly refractive or birefringent material divides into two rays: an

ordinary ray (or o ray or ω [omega] ray) and an extraordinary ray (or e ray or ε [epsilon] ray). Asthe name implies, the o ray behaves in an "ordinary" way, following Snell's law without a

problem. The ratio of the sine of the angle of incidence to the sine of the angle of ordinary

refraction is a constant. The e ray gets its name because it does not obey this rule.

falls apart here …

Birefringence is only a property of solids

When the incident angle is just right, the o and e rays will follow the same path and the

birefringence cannot be seen geometrically. At all other angles, the the two rays will follow

different paths. Thus, the index of refraction for extraordinary rays is also a continuous function



of direction. The index of refraction for the ordinary ray is constant and is independent of

direction

The index of refraction for the extraordinary ray is a continuous function of direction. The index

of refraction for the ordinary ray is independent of direction. The two indices of refraction are

equal only in the direction of an optic axis.

The measure of birefringence (δ) [delta] is the difference between the indices of refraction of the

two rays.

δ = ne − no

In some materials (like calcite) ne < no and the birefringence is less than zero (that is, the e ray is

refracted less than the o ray) and the material is said to be optically negative. In other materials

(like quartz) the reverse is true and these materials are said to be optically positive. Materials thatdo not show birefringence are said to be isotropic (like diamond); that is, they behave the same

no mater what the alignment of the crystal is relative to the incident ray.

optical behavior comment examples

isotropic (linear) single refraction gases, liquids, glasses, diamond

uniaxial negativedouble refraction

e ray travels fastercalcite, tourmaline, sodium nitrate

uniaxial positivedouble refraction

o ray travels fasterice, quartz, rutile

biaxial triple refraction mica, perovskite, topaz

optics is the study of the nature and behavior of light

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