Physics 21
Fall, 2011
Solution to HW28
3331
Unpolarized light of intensity 26.0 W/cm
2
is inci
dent on two polarizing filters. The axis of the first filter is at
an angle of 24.8
◦
counterclockwise from the vertical (viewed
in the direction the light is traveling) and the axis of the
second filter is at 65.0
◦
counterclockwise from the vertical.
What is the intensity of the light after it has passed through
the second polarizer?
When the unpolarized light (intensity
I
0
) passes through the
first polarizer, its intensity decreases by half and it will be
polarized in the same direction as the axis of the first po
larizer. Therefore the intensity after the first polarizer is
I
1
=
I
0
/2 = 13 W/cm
2
. The light is now polarized, so when
it passes through the second polarizer its intensity decreases
by another factor of cos
2
φ
, according to Malus’ Law:
I
2
=
I
1
cos
2
(
φ
)
,
where
I
2
is the intensity after the second polarizer, and
φ
is
the angle between the polarization of the light and the axis
of the polarizer.
Since the axis of the first polarizer is at
24.8
◦
, and the axis of the second polarizer is at 65.0
◦
in the
same direction, the angle between them is the difference, or
40.2
◦
. Then
I
2
= (13 W
/
cm
2
) cos
2
(40
.
2
◦
) = 7
.
58 W
/
cm
2
.
3458
Saturn is viewed through the Lick Observatory re
fracting telescope (objective focal length 18 m).
If the di
ameter of the image of Saturn produced by the objective is
1
.
7 mm, what angle does Saturn subtend from when viewed
from earth?
In the figure above (taken from page 1193 in the textbook),
it is shown that a refracting telescope is made of two lenses,
the objective and the eyepiece. Note that in this problem,
we are only dealing with the objective lens. Saturn’s average
distance from the earth is 1
.
433
×
10
12
m, which is very large
compared to the other distances in this problem, so we can
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 Spring '08
 Hickman
 Work, Light, Wavelength, tan θ

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