EE 119
Homework 2
Professor: Jeff Bokor
TA: Xi Luo
Due Tuesday
,
Feb
9
th
2010
(Please submit your answers in EE119 homework box located in 240 Cory Hall)
1.
(a) In class, the angle of deviation (
δ
) has been formulated for a prism with an
apex angle (
α
). Plot the angle of deviation (
δ
) versus incident angle for n = 1.5
and apex angle of 60°.
(b) The angle of deviation should have a minimum. Derive a general expression
for the incidence angle at which the deviation
δ
is minimized. Your answer
should be given as a function of the apex angle
α
and refractive index of the
prism. Show that the ray for which the deviation is a minimum traverses the
prism symmetrically. This means that the incident angle and the exit angle are
the same.
(Hint: Show cos(
θ
1
)/cos(
θ
2
’
) = cos(
θ
1
’
)/cos(
θ
2
), then make use of Snell’s law
once again. There are other ways to do this problem, so you don’t need to
follow the hint. )
(c) In the case when the angle of deviation is a minimum, find an expression for a
refractive index of the prism. Express the refraction index in terms of the
minimum angle of deviation
δ
m
and the apex angle
α
. This equation forms the
basis of one of the most accurate techniques for determining the refractive
index of a transparent substance.
(d) Now a prism (n = 1.5 at
λ
o
) with an apex angle of 4° is immersed in a liquid (n
= 1.3 at
λ
o
). If a laser beam at wavelength of
λ
o
passes through this prism and
is then reflected by a mirror (Fig. 1), how much do you need to rotate the
mirror so that the reflected beam is parallel to the incoming laser beam? Note
that here you have to modify the expression of
δ
given in the lecture note,
since that expression is derived for the case when the prism is in the air (n =
1).
4
o
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document2.
In birefringent crystals such as quartz, there exists a direction called the
optical
axis
. For light propagating in the crystal along a direction other than the optical
axis, its polarization can be decomposed into the
ordinary component
that is
perpendicular to the optical axis, and the
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '09
 Prism, Conan, Schmidt Prism

Click to edit the document details