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Physics 202
Assignment 12
Due at 11:00pm on Wednesday, April 23, 2008
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Geometry and Reflections
Description:
A case of reflection from multiple surfaces, basically a geometry review.
Learning Goal:
To learn and practice the geometry skills necessary for complex reflection setups.
The law of reflection has the very simple form
,
where
is the angle between the normal and the incident ray and
is the angle between the normal and the
reflected ray. Although the law itself is easy to use, many realistic situations involve successive reflections from multiple
surfaces. The law of reflection does not become any more complicated in such cases, but the geometry of the rays does become
complicated. Consider the case of light shining onto a mirror, which is attached to another mirror at some angle
, as shown in
the figure
. In this problem, we will find the angle at which light leaves the
arrangement of two mirrors.
Part A
If the light strikes the first mirror at an angle
, what is the reflected angle
?
Express your answer in terms of
.
ANSWER:
=
Part B
Now, find the angle
(shown in the new figure ) in terms of
.
You can easily find
in terms of
, then just substitute your
expression from Part A.
Hint B.1
Relationship between
and
and
are complementary angles.
Express your answer in degrees in terms of
. Notice that the degrees symbol is already listed for you, so just use the
number "23" to indicate 23 degrees.
ANSWER:
=
[
P
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Part C
Now, find the angle
shown in the figure in terms of
and
.
Hint C.1
Angles in a triangle
The sum of the angles in a triangle is
.
Express your answer in degrees in terms of
and
.
ANSWER:
=
Part D
Find the angle
shown in the figure in terms of
and
. You
will need to assume that
, as it appears in the picture.
Hint D.1
Relationship between
and
and
are complementary angles.
Hint D.2
How to find
in terms of
You can find
in terms of
by using the law of reflection.
Express your answer in degrees in terms of
and
.
ANSWER:
=
Virtually any reflection problem, no matter how intimidating it may seem, can be broken down into simple parts by
considering each individual reflection carefully.
Is Light Reflected or Refracted?
Description:
Mostly conceptual questions on index of refraction and Snell's law. Last few parts deal with total internal
reflection.
When light propagates through two adjacent materials that have different optical properties, some interesting phenomena occur
at the interface separating the two materials. For example, consider a ray of light that travels from air into the water of a lake. As
the ray strikes the airwater interface (the surface of the lake), it is partly
reflected
back into the air and partly
refracted
or
transmitted into the water. This explains why on the surface of a lake sometimes you see the reflection of the surrounding
landscape and other times the underwater vegetation.
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 Spring '09
 All
 Snell's Law, Total internal reflection, Geometrical optics

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