Electromagnetic Waves- Transverse waves

- Travel at the speed of light

- Can travel in a vacuum

-Created by alternating electric and magnetic fields.

-James Maxwell created radio waves by passing an alternating current through a wire.

Visible range – from approx 400 nm to 700 nm

- red has the lowest frequency and highest wavelength

Properties of EM Waves

Dispersion – white light is separated into the visible spectrum

Red is dispersed the least, violet the most

The lowest wavelength refracts the most.

Depending on the frequency of the EM wave and what substance it is hitting, the wave will be transmitted or absorbed.

Transmission – the wave will pass through the substance.

Ex. X-rays will pass through most solidsLight will pass through air

Absorption – the wave will be absorbed and excite the substance

Ex. Microwaves are absorbed by water molecules

UV is absorbed by the ozone layer

White light hitting a blue filter. Some light is reflected, blue light is transmitted while the other colors are absorbed.

The intensity (brightness) of light is indirectly related to the distance to the source squared.

Scattering - light will be scattered by particles in the airRed scatters least, blue scatters most

Example – Blue sky, red sunsets

LASERLight Amplification by the Stimulated Emission of Radiation

Monochromatic (one color) coherent (same frequency, in phase) light

Population inversion

Interference and diffraction

Light falling on two slits will produce an interference pattern(Young’s two-slit experiment)

ndd

nD

xd

n

D

xd

nd

Ds

sin

)1(

sin

The equations of interference patterns:

Path difference

s = lD/d

s = how far apart maxima areD = distance from slits to screend = distance between slits

A source of light of unknown wavelength is used to illuminate two very narrow slits a distance 0.15 mm apart. On a screen at a distance of 1.30 m from the slits, bright spots are observed separated by a distance of 4.95 mm. What is the wavelength of the light being used?

571 nm

Two narrow slits 0.01 mm apart are illuminated by a laser of wavelength 600 nm. Calculate the fringe spacing on a screen 1.5 m from the slits.

Diffraction grating

d sin q = n l

Light of wavelength 680 nm falls on a diffraction grating that has 600 lines per mm. What is the angle separating the central maximum (n=0) from the next (n=1)?

q = 24.1o

Red light (wavelength = 700 nm) is shone through a grating with 300 lines/mm.

a)Calculate the diffraction angle of the first red line.

b)Calculate the diffraction angle of the second red line.

Optical instrumentsConverging lens

A lens that is thicker in the middle than at the edges. Light is refracted toward the principal axis (the straight line that goes through the center at right angles to the lens surface).

Parallel rays will refract to a point on the principal axis called the focal point. The distance from the lens to the focal point is the focal length.

Optometrists describe the power of a lens as

P = 1/f

Example: A lens with a focal length of 25 cm would have a power of 4.0

Real image – an image that is created by rays of light passing through a lens

- can be projected on a screen

- inverted

Virtual image – rays do not actually meet, only their mathematical extensions do

- cannot be projected on a screen

- upright (erect)

Ray diagrams – pictures used to identify what kind of image will be created by a lens.

Rays to draw

1) Parallel rays refract through the focus

2) Rays through the center continue straight thru

3) Rays thru the focus refract parallel

Where these rays meet describe the image. Only two rays are necessary.

Using graph paper, draw a ray diagram for an object a) at 2F, b) between F and 2F, c) at F and d) inside F

This can also be done mathematically with the thin lens formula.

1/f = 1/v + 1/u u = object distance

v = image distance

Image distance : (+) means real image, (-) means virtual

Also the magnification can be calculated.

m = hi/ho = -v/u

A converging lens has a focal length of 15 cm. An object of height 2 cm is placed 60 cm from the lens. Determine the image.

An object is placed 15 cm in front of a converging lens of focal length 20 cm. Determine the image.

A diverging lens causes light to refract AWAY from the focus.

What kind of image does a diverging lens create?

Virtual only

The TelescopeThe refracting telescope works by bending light with two lenses.  The objective lens makes a small real image of the object while the eyepiece lens acts as a magnifying glass. 

The focal points of the two lenses should be at the same point to produce a focused image.

Draw a ray diagram for a telescope. Note where the objective lens focuses the light from a star and where the final image is located and in what direction.Step 1: Draw the lenses and axis (no foci)Step 2: Draw a ray passing through the center of the objective hitting the eyepiece halfway downStep 3: Draw two more rays entering the objective at the same angle as the first. The top ray should hit the bottom of the eyepiece.

Step 4: The bottom ray will cross where the other two intersect. This is the focus. Draw in the first image.Step 5: The rays emerge from the eyepiece parallel. To find the angle draw a dotted line from the top of the image through the center of the eyepiece

The angular magnification can be worked out by the simple formula: where qi and qo are small angles in radians. •The angle qi is the angle subtended by the object to the unaided eye. •The angle qo is the angle subtended by the image to the eye.

The magnification can also be shown to be related to the focal lengths of the lenses by:

o

iM

e

o

f

fM

In a telescope the eyepiece has a focal length of 2 cm and the objective has a focal length of 220 cm.  What is the magnification? 

Magnification = fo/fe = 220/2 = 110

If the moon subtends an angle of 8.8 x 10-3 rad to the naked eye, what would the angle be for the image of the moon observed through the telescope? 

Angle subtended by the Moon = 8.8 x 10-3 rad x 110 = 0.97 rad

A telescope is constructed from two lenses: an objective lens of focal length 100 cm and an eyepiece of focal length 10 cm. The telescope is used in normal adjustment.

a) Calculate the angular magnification

b) What is the distance between the lenses?

Microscope – similar to a telescope except that

a) The focal points of the two lenses are NOT at the same point

b) The image from the objective lens is formed inside the focal length of the eye piece.

c) The object is located very close to the objective lens

Step 1: Draw the lenses and an axis.Step 2: Draw a ray through the center of the objective to a point halfway down the eyepiece. Draw an object a short distance from the objective.Step 3: Draw a parallel ray from the object to the objective. Continue this ray to the bottom of the eyepiece. Mark Fo at the point where this ray crosses the axis. Construct an image at the place where the two rays intersect.

Step 4: Draw a dotted line from the top of the first image through the middle of the eyepiece.Choose a point on this line beyond the objective and draw the rays coming from this point.

Aberrations – there are two flaws inherent in all lenses that must be corrected for perfect images.

Spherical aberration

Rays hitting the very edge of a lens do not focus to the exact same spot as most of the light.

Correcting: Using an aperature to block the light hitting the edges of the lens

Cameras, eyeballs

Chromatic aberration

Because different wavelengths of light (colors) refract slightly differently, not all of the colors focus at the some exact point.

Solution: making a lens out of two different materials so that one material fixes the other. This is called an achromatic doublet.