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...
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,