When light passes through a prism, the angle that the refracted ray makes relative to the incident ray is called the deviation angle δ , Fig. 32-64. Show that this angle is a minimum when the ray passes through the prism symmetrically, perpendicular to the bisector of the apex angle ϕ , and show that the minimum deviation angle, δ m , is related to the prism’s index of refraction n by n = sin 1 2 ( ϕ + δ m ) sin ϕ / 2 . [ Hint : For θ in radians, ( d / dθ )(sin −1 θ ) = 1 / 1 − θ 2 . ] FIGURE 32-64 Problems 79 and 80.
When light passes through a prism, the angle that the refracted ray makes relative to the incident ray is called the deviation angle δ , Fig. 32-64. Show that this angle is a minimum when the ray passes through the prism symmetrically, perpendicular to the bisector of the apex angle ϕ , and show that the minimum deviation angle, δ m , is related to the prism’s index of refraction n by n = sin 1 2 ( ϕ + δ m ) sin ϕ / 2 . [ Hint : For θ in radians, ( d / dθ )(sin −1 θ ) = 1 / 1 − θ 2 . ] FIGURE 32-64 Problems 79 and 80.
When light passes through a prism, the angle that the refracted ray makes relative to the incident ray is called the deviation angle δ, Fig. 32-64. Show that this angle is a minimum when the ray passes through the prism symmetrically, perpendicular to the bisector of the apex angle ϕ, and show that the minimum deviation angle, δm, is related to the prism’s index of refraction n by
n
=
sin
1
2
(
ϕ
+
δ
m
)
sin
ϕ
/
2
.
[Hint: For θ in radians, (d/dθ)(sin−1θ) =
1
/
1
−
θ
2
.
]
63 In Fig. 33-60, light enters a 90°
triangular prism at point P with inci-
dent angle 6, and then some of it
refracts at point Q with an angle of
refraction of 90°. (a) What is the in-
dex of refraction of the prism in
terms of 6? (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?
Figure 33-60 Problem 63.
63 In Fig. 33-60, light enters a 90°
triangular prism at point P with inci-
dent angle 0, and then some of it
refracts at point Q with an angle of
refraction of 90°. (a) What is the in-
dex of refraction of the prism in
terms of 0? (b) What, numerically,
Air
Q
Figure 33-60 Problem 63.
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?
53 SSM www ILW In Fig. 33-53, a ray is incident on one face
of a triangular glass prism in air. The angle of incidence e is chosen
so that the emerging ray also makes the same angle e with the nor-
mal to the other face. Show that the index of refraction n of the
glass prism is given by
sin ( + 6)
sin o
where o is the vertex angle of the prism and is the deviation
angle, the total angle through which the beam is turned in passing
through the prism. (Under these conditions the deviation angle u
has the smallest possible value, which is called the angle of mini-
mum deviation.)
Figure 33-53 Problems 53 and 64.
Chapter 32 Solutions
Physics for Scientists and Engineers with Modern Physics
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