PHYS 222
Worksheet 28 – Polarization
Supplemental Instruction
Iowa State University
Leader:
Course:
Instructor:
Date:
Alek Jerauld
PHYS 222
Dr. Paula Herrera-Siklódy
4/5/12
Useful Equations
I  I0 cos2 
Law of Malus. Light passing through a polarizer
Natural light is usually denoted as I0 – when going through a single filter, intensity is
reduced to ½ original intensity
Related Problems
1) A beam of unpolarized light of intensity I0 passes through a series of ideal polarizing
filters with their polarizing directions turned to various angles as shown in the figure. (Book
33.25)
(a) What is the intensity at each of the 3 points?
I
IA  0
2
IB 
I0
I
cos 2 (60)  0
2
8
I0
3I
cos 2 (60) cos 2 (90  60)  0
2
32
(b) If the middle filter was removed, what will be the light intensity at point C?
I
I C  0 cos 2 (90)  0
2
IC 
2) A beam of polarized light passes through a polarizing filter. When the angle between the
polarizing axis of the filter and the direction of polarization of the light is θ, the intensity of
the emerging beam is I. If you now want the intensity to be I/2, what should be the angle (in
terms of θ) between the polarizing angle of the filter and the original direction of polarization
of the light? (Book 33.29)
I cos 2 1 
I1  I 0 cos 2 1  I 2  I 0 cos 2 1  cos 2  2   0
2
 cos 1  
  2  cos 1 

2 

3) Unpolarized light of intensity 21.2 W/cm2 is incident on two polarizing filters. The axis of
the first filter is at an angle of 24.6 degrees counterclockwise from the vertical (viewed in
the direction the light is traveling) and the axis of the second filter is at 62.2
degrees counterclockwise from the vertical. What is the intensity of the light after it has
passed through the second polarizer? (Book 33.31)
I1 
I0
2
I 2  I1 cos 2    
I0
cos 2     6.65 W / cm2
2
4) Three polarizing filters are stacked, with the polarizing axis of the second and third filters
at angles of 23.6 degrees and 62.2 degrees, respectively, to that of the first. If unpolarized
light is incident on the stack, the light has an intensity of 75.5 W/cm2 after it passes through
the stack. If the incident intensity is kept constant, what is the intensity of the light after it
has passed through the stack if the second polarizer is removed? (Book 33.34)
I
I 3  0 cos 2  2  cos 2 3   2   75.5 W / cm 2
2
 I 0  294.416
I3 ' 
I0
cos 2 3   32.02 W / cm 2
2