Lehigh University
Physics 21, Spring 2008
April 2, 2008
HW23 Solutions
231.
(HRW 3367)
In Fig.
3365
, light enters a 90°
triangular prism at point P with incident angle
, and then
some of it refracts at point Q with an angle of refraction of
90°. (a) What is the index of refraction of the prism in terms
of
? (b) What, numerically, is the maximum value that the
index of refraction can have? Does light emerge at Q if the
incident angle at P is (c) increased slightly and (d)
decreased slightly?
Solution:
67. (a) A ray diagram is shown below.
Let
θ
1
be the angle of incidence and
θ
2
be the angle of refraction at the first surface. Let
θ
3
be the angle of incidence at the second surface. The angle of refraction there is
θ
4
=
90°. The law of refraction, applied to the second surface, yields
n
sin
θ
3
= sin
θ
4
= 1. As
shown in the diagram, the normals to the surfaces at
P
and
Q
are perpendicular to each
other. The interior angles of the triangle formed by the ray and the two normals must sum
to 180°, so
θ
3
= 90° –
θ
2
and
sin
sin
cos
sin
.
θ
θ
θ
θ
3
2
2
2
2
90
1
=
°−
=
=
−
b
g
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 Spring '08
 Kim
 Light, Snell's Law, Total internal reflection, Geometrical optics

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