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How
Waves Interact
Interference
is what happens when waves interact with each other. The waves can
be waves in a swimming pool, sound waves flowing through air, or
even light waves. (Don't be confused by the colors of our waves.
They do not relate to the color of light. It is just a convenient
way to identify them.)
 Imagine
that you have a wave (the wave could be anything) that looks
like the red line. You can see that the hills and troughs of
the wave are rather shallow. In physics, we call the distance
from the highest point to the lowest point amplitude.
Since your wave is shallow, you can say that it has a small
amplitude. Then along comes another wave, the blue wave. The
blue wave has a larger amplitude. On our chart, both of the
waves line up, meaning that they both have the same length (wavelength),
and cross the axis at the same point in the same direction (here,
down-right). Because of this we say that the two waves are in
phase. When the red wave and the blue wave interact, you
get a single wave--the yellow wave. The hills of the blue wave
added to the hills of the red wave, and the troughs of the blue
wave subtracted from the troughs of the red wave. This is called
constructive interference: the blue wave reinforced the features
of the red wave. |
 If
the waves were out of phase, the hills of the blue wave
would still be added, and the troughs still subtracted, but
it would have reinforced the opposite features on the red wave.
The hill would cancel out the trough. This is called destructive
interference. The result of two identical waves (such as
these) out of phase is a straight line. |
Make sure you see the Interactive
Interference Illustration, which lets you play with interference
first hand.
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Diffraction
Grating
A
wave of light passing through a slit in a diffraction grating.
The image projected on the screen (the wall opposite the slit) directly across from the slit. Intensity of the image fades off on either side (not exactly visible here). |
A diffraction grating
is a slit (or slits) in a wall designed to allow a wave to pass
through. This wave is then diffracted, causing it to move
out from the slit in all directions. Notice in the illustration
on the left that the wave reaches every point on the far wall as
it travels out and away from the slit. Let's say that the wave we
were discussing is light from a projector, the diffraction grating
is a slide in the projector with a small slit in it, and the far
wall is actually a screen. If the grating only has one slit, the
image on the screen would be a solid line, since the wave reached
the wall uninterrupted.
A
wave of light passing through two slits in a diffraction grating,
causing interference.
The image projected on the screen. |
If the grating has two
or more slits the waves would constructively and destructively interfere
with each other at regular intervals. This would create a banding
effect on the screen. The location of each band of light can be
calculated mathematically. Let's say:
• d is the distance
between the center of the slits
• m is the order of the band in question. The center band is 0th
order band, the first band on either side is the 1st order band,
etc.
•  (read theta) is
the angle of diffraction (the angle made by the slit, the wall,
and the band of light representing constructive interference)
•  (read
lambda) is the wavelength
d sin
= m
As you can
imagine, this equation is useful for finding out many things. For
example, if you know the distance to the screen, the distance between
slits, and the wavelength of the light, you can solve for
, the angle, and find
the distance to any one of the bands.
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