Modern Optics Lab
Lab 5 Part 1: Experiments involving Light Polarization
Topics
 Measuring light transmission through a dichroic material (“polarizer
sheet”) as a function of polarization angle to verify Malus’ Law
 Using polarization by reflection to determine the Brewster angle and then
calculate the index of refraction of the reflecting material.
 Qualitative observation of light polarization by scattering.
Modern Optics Lab
Lab 5 Part 1: Experiments involving Light Polarization
Linearly polarized light
Modern Optics Lab
Lab 5 Part 1: Experiments involving Light Polarization
Dichroic Absorption
Passes
Is absorbed
Partially absorbed
and partially passes
Modern Optics Lab
Lab 5 Part 1: Experiments involving Light Polarization
Dichroic Absorption
Partially absorbed and partially passes

E||
E

E
E||  E cos
Intensity E
2
Transmitte
d Intensity E  E cos 
2
||
(Malus’ Law)
2
2
Modern Optics Lab
Lab 5 Part 1: Experiments involving Light Polarization
Polarization Dependent Reflection
ni
i
r
i : incidentangle

nt
t
r : reflectedangle
t : transmitted angle
  180 r  t
Incident plane: Plane that contains incident, reflected and transmitted ray.
Modern Optics Lab
Lab 5 Part 1: Experiments involving Light Polarization
Polarization Dependent Reflection
ni
“Parallel polarized” light.
(parallel to incident plane)
“p-polarized”
(p as in “parallel”)
nt
Incident plane: Plane that contains incident, reflected and transmitted ray.
Modern Optics Lab
Lab 5 Part 1: Experiments involving Light Polarization
Polarization Dependent Reflection
ni
“Perpendicular polarized” light.
(perpendicular to incident plane)
“s-polarized”
(s as in “senkrecht”)
nt
Incident plane: Plane that contains incident, reflected and transmitted ray.
Reflection Coefficients:
Modern Optics Lab
Lab 5 Part 1: Experiments involving Light Polarization
Fresnel Equations
Reflection coefficients (relate to Electric field strength ratios)
For parallel polarized light:
 E0 r
r||  
 E0i
 nt cos i  ni cos t tan i   t 
 

|| nt cos i  ni cos t tan i   t 
For perpendicular polarized light:
E 
n cos  i  nt cos  t sin  i   t 
r   0 r   i

 E0i   nt cos  i  ni cos  t sin  i   t 
Modern Optics Lab
Lab 5 Part 1: Experiments involving Light Polarization
Reflection Coefficients
0.4
Reflection Coefficient
0.2
0
-0.2
r parallel
r perpendicular
-0.4
-0.6
-0.8
-1
0
20
40
60
80
Angle of Incidence in Degrees
100
Modern Optics Lab
Lab 5 Part 1: Experiments involving Light Polarization
Reflectances (relate to intensity ratios):
tan2 i  t 

tan2 i  t 
R||  r|| 
2
R  r 
2
sin 2 i  t 

sin 2 i  t 
Modern Optics Lab
Lab 5 Part 1: Experiments involving Light Polarization
Reflectances
1
Reflectance
0.9
0.8
0.7
0.6
0.5
R parallel
R perpendicular
0.4
0.3
0.2
0.1
0
0
20
40
60
80
100
Angle of Incidence in Degrees
Brewster angle: R||=0
R||  r|| 
2
tan2 i  t 
2
i  t     i  t  90    90


tan
2
tan i  t 
Modern Optics Lab
Lab 5 Part 1: Experiments involving Light Polarization
i   Brewster
Brewster Angle
ni
90 
“Parallel polarized” light
is not reflected at all if
incident under the
“Brewster Angle”
nt
sin i
sin i
sin i
nt sin t  ni sin i  nt  ni
 ni
 ni
 ni tani
sin t
sin 90  i 
cosi
nt  ni tani
Modern Optics Lab
Lab 5 Part 1: Experiments involving Light Polarization
i   Brewster
Reflected light is s-polarized
under the Brewster angle.
ni
90 
nt
Modern Optics Lab
Lab 5 Part 1: Experiments involving Light Polarization
Radiation pattern from an accelerated charge
e-
Radiation is polarized
Modern Optics Lab
Lab 5 Part 1: Experiments involving Light Polarization
Radiation pattern from an accelerated charge
e-
Length of arrow indicates intensity in that direction
Modern Optics Lab
Lab 5 Part 1: Experiments involving Light Polarization
Scattered light
nothing scattered in this direction
incoming light
scattered light
e-
nothing scattered in this direction
Modern Optics Lab
Lab 5 Part 1: Experiments involving Light Polarization
Scattered light
nothing scattered
in this direction
incoming light
scattered light
e-
nothing scattered
in this direction
Modern Optics Lab
Lab 5 Part 1: Experiments involving Light Polarization
Scattered light
polarized
polarized
incoming lightunpolarized
scattered light
e-
Modern Optics Lab
Lab 5 Part 1: Experiments involving Light Polarization
Rayleigh Scattering
1  cos   2 
Intensityof scatteredlight  I  I o


2R 2   
2
4
2
 n 1   d 
 2
  
n 2  2 
2
6
n  index of refractionof particle
d  diameterof particle
incoming light

R  distanceto particle
Modern Optics Lab
Lab 5 Part 1: Experiments involving Light Polarization
Intensity of scattered light
  90  1  cos2   1
  90  1  cos2   1
incoming lightunpolarized
  180  1  cos2   2
  0  1  cos2   2
e-
  90  1  cos2   1
  90  1  cos2   1
1  cos   2 
I  Io


2R 2   
2
4
2
 n 1   d 
 2
  
n 2  2 
2
6
Modern Optics Lab
Lab 5 Part 1: Experiments involving Light Polarization
Color of scattered light
4
incoming light
assume equal
color intensity
2
1  cos2   2   n 2  1   d 
  
I  Io

  2
2
2R
   n 2  2 
6
Scattered light
Unscattered light
Looking
at sky
above
Looking
at sunset
Modern Optics Lab
Lab 5 Part 1: Experiments involving Light Polarization
Experimental Details: Using the Photometer to Measure Intensity
“Zero” adjustment:
 Start with “Sensitivity” 1000 (least
Sensitive)
 Close off “Probe Input” with rubber
stopper so that no light enters.
 Use Zero Adjust button to get
needle to zero.
 Go to more sensitive setting (lower
number) and zero, etc.
Probe
Input
Sensitivity
300
1000
Variable
3
1
CAL.
Zero
Adjust
Measurement of Intensity:
 Start with “Sensitivity” 1000 (least
Sensitive)
 Plug fiber optic cable into “Probe
Input”.
 Step by step increase sensitivity
but make sure needle stays within
range.
See pages 19 ff of the “Advanced Optics Manual” for detailed operating instructions!!
Modern Optics Lab
Lab 5 Part 1: Experiments involving Light Polarization
V.A Dichroic Absorption
Is the laser polarized?
Polarizer
Laser
Screen
Modern Optics Lab
Lab 5 Part 1: Experiments involving Light Polarization
V.A Measuring I(Q) and verifying Malus’ Law
 Zero Photometer
 Attach fiber optic cable to photometer and to rotational stage (tighten screw only very
lightly otherwise fiber optic cable may break internally). Do not bend fiber optic cable
too tightly.
Top view
Polarizer
Laser
 Measure I(Q).
 Plot I(Q) versus cos2Q.
Fiber Optic Cable
Photometer
Modern Optics Lab
Lab 5 Part 1: Experiments involving Light Polarization
V.A Measuring I(Q) with two polarizers
Polarizer 2 ( to laser polarization)
Polarizer 1
Laser
 Vary the orientation Q1 of polarizer 1.
 Measure I(Q1) plot versus Q1 .
 Explain results.
Screen
Modern Optics Lab
Lab 5 Part 1: Experiments involving Light Polarization
V.B Orienting the laser polarization to be horizontal
 Rotate laser so that E-vector is horizontal (from V.A. you should know approximate
orientation already).
 With polarizer oriented as shown, fine tune the laser orientation until light
transmission is minimized.
Polarizer (0-180 direction vertical)
Laser
Screen
Top view
Modern Optics Lab
Lab 5 Part 1: Experiments involving Light Polarization
V.B Adjusting the glass plate
 Front surface of glass plate should be hit by laser exactly at the rotation axis of the
rotation stage.
 Calibrate the zero degree position by using the back-reflection of the laser.
Top view
Glass plate
Polarizer (0-180 direction vertical)
Laser
Short component holder
Modern Optics Lab
Lab 5 Part 1: Experiments involving Light Polarization
V.B Finding the Brewster angle
 Rotate until reflection intensity is minimized to find the Brewster angle.
 Calculate the index of refraction of glass from the Brewster angle.
Top view
Polarizer (0-180 direction vertical)
Laser
Screen
Modern Optics Lab
Lab 5 Part 1: Experiments involving Light Polarization
V.B Adjusting the glass plate
 Front surface of glass plate should be hit by laser exactly at the rotation axis of the
rotation stage.
 Adjust 127mm lens so that sharp image of filament is seen on back side of lens
holder.
 Adjust glass plate orientation so that filament image is in the middle of lens holder.
127mm lens
Glass plate
Top view
Incandescent Light
Filament image
Short component holder
200mm
Approx.330mm
Approx.750mm
Modern Optics Lab
Lab 5 Part 1: Experiments involving Light Polarization
V.B Adjusting lens position and getting Brewster angle
 Rotate rotational stage by approx. 30 degrees.
 Readjust lens position so that filament is in focus on the screen.
 With polarizer select parallel polarization component. Look at intensity versus incident
angle. Then do the same for perpendicular polarization component.
 Make a qualitative comparison of I(Q) for the two components.
 Determine the Brewster angle again.
127mm lens
Top view
Incandescent Light
Polarizer
Screen
Modern Optics Lab
Lab 5 Part 1: Experiments involving Light Polarization
V.C Polarization by Scattering
 Front surface of glass plate should be hit by laser exactly at the rotation axis of the
rotation stage.
 Adjust 127mm lens so that sharp image of filament is seen on back side of lens
holder.
 Adjust glass plate orientation so that filament image is in the middle of lens holder.
48mm lens
Screen
Top view
Incandescent Light
Approx. 4cm
Murky water
Look from side (and look from top)
through polarizer
Modern Optics Lab
Lab 5 Part 1: Experiments involving Light Polarization
V.C Scattering of polarized laser light
 Look from side (and then from top down).
 Observe scattered light intensity as you rotate the laser’s polarization.
Screen
Top view
Laser
Murky water
Look from side (and look from top)
through polarizer