Class_Notes

Wave Interaction with Matter...

Refraction...

Are you ready to take the lifeguard test?... if you pass this test you know the law of refraction.

You are the lifeguard at point A on the sandy beach. A swimmer at point B in the water calls for help... Find the path you would take from point A to point B.

And, what principle of "lifeguarding" did you use?

Waves use the same principle... Traveling at different velocities in each medium, we take that path that will take THE LEAST TIME...

The velocity of light in air is 3 x 108 m/s... The velocity of light in water is 3/4 of its velocity in air. The velocity of light in glass is 2/3 of its velocity in air. Each material is given an "Index of Refraction, n" which is defined by

n = velocity in air / velocity in medium

Thus nwater = 4/3 = 1.33 nglass = 3/2 = 1.5

Since for waves... v = f l in each medium and

vair = f air lair and vwater = f water lwater

nwater = 1.33 = vair /vwater = f air lair /f water lwater

But the frequency does not change so it will cancel out... Thus the velocity is lower in water than in air and the wavelength is also smaller in water than in air...

Note that the angle in water, qwater is smaller than the angle in air, qair... Now trace the rays coming from the source S, which is under the water, up to the surface... remembering that the angle in air is greater than the angle the ray in water makes with the normal to the surface in the drawing below.

Total Internal Reflection

If light is introduced into the end of a glass tube and hits the side at angle greater than the critical angle, then it will reflect back into the tube and be travel inside the tube.

This is the basic principle for fiber optics. A laser beam in a fiber of diameter of a strand of hair can simultaneously carry about 10,000 phone calls.

What does the eye in the water see of the person sitting on the edge of the pool?

Another example of Refraction... Dispersion...

When white light enters glass, different colors bend different amounts (meaning that different colors travel at different velocities in glass but all travel at the same velocity in air).

The ultimate in refraction, reflection, refraction... THE RAINBOW

Lenses... creating images with refraction...

Basic properties of lenses... the focal point... where parallel rays converge....

There is a focal point on each side of the lens... finding images formed by lens... follow the rules...

Interference

What happens when two waves cross over each other... Simple basic rule... ADD THEIR AMPLITUDES as they cross...

Consider circular waves on the surface of water... let the dark circles represent the troughs and the bright circles represent the crests. Now suppose we have two such waves produced side by side as seen below.

In each of the interference patterns above, mark the points where a crest is on top of a crest with a dot and the points where a trough is on top of a trough with a dot... connect the row of dots.. These are regions of "Constructive Interference". Note that the spaces between the lines connecting the dots are lines where crests are on top of troughs... These are regions of "Destructive interference"...

Now we will examine how holograms are made...

Transmission Hologram

Two coherent laser beams are created with a beam splitter. One beam, the REFERENCE beam illuminates the film. The second beam, the OBJECT beam illuminates the OBJECT. Each point of the object then reflects the object beam to the film where it interferes with the reference beam. The reflected beam from one point is shown in the drawing above. The dark lines shown in the film are the crests of the interference pattern.

To view the image in the film, the same laser beam is shined on the hologram from the same angle and one view the image looking through the film at the position where the object had been placed when making the hologram. The pattern in the film deflects the laser light into the eye "as if" it was coming from the image... See viewing of image in diagram below.

White Light Hologram

Other applications of interference...

Standing Waves...

On Strings... the stringed instruments.

The oscillator at left vibrates at frequency, f, and sends wave down the string which reflects off of pulley at right end and the two waves traveling in opposite directions cause a standing wave pattern IF...

v = f l and the Length of the string is an integral number of half-wavelengths

L = n l / 2 which means that the waves must travel with a velocity

v = f 2 L / n

The velocity of the wave is dependent on the tension, T = m g, in the string and the mass per unit length, m, of the string...

Notes:

As the number of nodes is adjusted by changing the mass, m, on the string, the frequency goes up as the number of loops decreases.

The loops are one half wavelength long... the nodes are points where the waves always cancel each other as they pass those points. There will be standing wave patterns ONLY when there is the appropriate combination of velocity, wavelength, and frequency.

On Tubes... the wind instruments.

Displacement node at closed end and antinode at open end.

On surfaces... the percussion instruments.

Displacement nodes where surface is clamped... ex. edges of drum

Other standing wave examples.

wind chimes, car antenna, keys on key chains, building during earthquake, Tacoma Narrows bridge,