Class_Notes

Wave Interaction with Matter...

Reflection:

Law of Reflection... Do you know how to dribble a basketball?... Same Law...

ANGLE OF INCIDENCE = ANGLE OF REFLECTION

How could you determine the path light would take from point a to point b after hitting the mirror?

Note that if we had reversed the direction of light in either case, the paths taken by the light would be the same... this is called the "reversibility principle".

IMAGES FORMED BY MIRRORS

The eye traces a ray back along the line of entry... and thinks that the source is somewhere along that line...... if we use both eyes and trace two rays back along the rays entering the eye... we call the point of intersection of those rays as the image point....

We can see that the image is NOT IN the mirror but behind the mirror... Can you show that, in a plane mirror, the image is just as far behind the mirror as the object is in front?

Suppose the object is off the edge of the mirror... will it still have an image?

Full-length mirror... what did you find from the exploratory?...

Does it depend on your distance from the mirror?

How long must the mirror be?

What about the wall behind you?

Draw the images of the person in the tilted mirror and the number 7 in the mirror on right and show the rays that enter the eye from each image.

Double mirror...

Where are the images? What are the rules?

How do you see the images? Draw a line from each image to the eye then trace it back, obeying the law of reflection till you get back to the object.

Curved Mirror...

Applying the law of reflection to a curved mirror... the first step is to identify a special point called the focal point, the point at which parallel rays of light will be meet after reflecting off the mirror... in the diverging mirror we must trace back the reflected waves to find the focal point.

Note that a ray going through the focal point will come out parallel to the axis of the mirror.

Now we can find the image of a real object.... and see why the rear-view mirror on the car has the message: "Objects are closer than they APPEAR to be"... Draw two rays (one parallel to the axis and one through the focal point) to find the image of the the tip of the arrow.

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.

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...

Other applications of interference...

Standing Waves...

On Strings... the stringed instruments.