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The figure on the left shows light bending toward
the normal as it enters the denser medium of water. Explain why
the light bends in this direction using physical arguments rather than
any equations. |
|
As described earlier in the module,
the edge of the wavefronts closest to the water slows down first.
Since the edge away from the water is still moving at the faster speed,
the wavefront swings around and becomes more parallel to the surface.
This makes the direction of motion more parallel to the normal. |
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Which angle, θ2
measured in the water or θ1
measured in air, will be greater if the light bends toward the normal? |
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Looking at the figure, we can see
that the angle measured in air, θ1,
will be larger; the angle decreases in a denser medium. |
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Will a denser medium have a larger or a smaller index
of refraction than a rarer medium? |
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A denser medium provides more matter
from which the light can scatter, so light will travel more slowly in a
dense medium. A slower speed means a higher index of refraction,
so n2 > n1,
as indicated in the image on the left. |
|
Use Snell's Law combined with your answer to the previous
question to mathematically predict which angle will be greater when light
moves into a denser medium. How does this compare with your answer
to the second question that was based on physical arguments? |
|
Snell's Law says
n1
sin θ1 = n2
sin θ2, so
n1/n2
= (sin θ2)/(sin
θ1)
In our situation,
n1/n2
< 1, so
(sin θ2)/(sin
θ1)
<1.
For angles less than 90 degrees, sin
increases with angle, so
θ2
< θ1.
This is consistent with what the figure
and physical arguments indicate. |
|
Use Snell's Law to predict what will happen to the light
as it enters the water if it approaches the surface along the normal to
the surface, as shown in the figure on the right. |
|
If the light approaches along the
normal, the angle of incidence between the light and the normal is
θ1
= 0.
Snell's Law then gives
sin θ2
= (n1/n2)
sin θ1 = 0
θ2
= 0 = θ1.
The light does not bend when it enters
a new medium along the normal. |
|
Now explain why this occurs using physical arguments
rather than equations. |
|
If the light travels along the
normal, the wavefronts are parallel to the surface. Since no point
on a wavefront enters the denser medium earlier than any other point on
the wavefront, no bending occurs. |
