Chapter 34 : The Wave Nature of Light

Interference and Polarization

Thin Film (Summary)

Reflected Ray : Ray reflecting off an interface:
• picks up a sign flip if reflecting off a higher 'n' material
• no sign change if reflecting off a lower 'n' material
Transmitted Ray : Ray passing through an interface:
• no sign change, no matter what the 'n' values are
Wavelength Changes while the photon is in the 'film'
• λ_film = λ_o/n_film

IF THE REFLECTED RAYS HAVE THE SAME SIGN:
\[ 2t = (m)\lambda_{film} \hspace{3em} (constructive) \]

\[ 2t = (m+\frac{1}{2})\lambda_{film} \hspace{3em} (destructive) \]

IF THE REFLECTED RAYS HAVE OPPOSITE SIGNS:
\[ 2t = (m+\frac{1}{2})\lambda_{film} \hspace{3em} (constructive) \]

\[ 2t = (m)\lambda_{film} \hspace{3em} (destructive) \]

Which equation to use depends on BOTH:
• What is the film doing to the light?
• What do we want/need to happen to this light? (Equally important!)

Lens Coating

Example (from Test 3 practice problems) :
A lens (made of glass with n=1.56) has a thin coating applied to it (the coating has an index of refraction of n=1.25).
When white light reflects off the lens it appears greenish-yellow (λ = 570 nm) in color.
How thick is the coating on the lens? (Give the thinnest two possible thicknesses it might be.) (Be sure to draw a diagram showing any sign-flip(s) involved here and be sure to explain how/why you decided to use the equation you chose to analyze this problem.)

Phone Screen Protector

Suppose we put this same film on our phone. What effect would it have? (The light source is coming from the phone screen itself now, passing through the glass, then hitting the film and then finally reaching our eyes.)
What colors (coming from the screen) would we see as extra bright or dim?
First Though : What equations would apply here? What equation would yield constructive interference for the light heading towards our eyes?

That seems like a pretty negative side effect of adding a screen protector to the phone. Why do we not see this effect?

Actual (plastic) screen protector thickness: 0.1 mm
Actual (glass) screen protector thickness: 0.3 mm to 0.5 mm
How many wavelengths does that represent?

POLARIZATION

Light (or any EM wave) can be polarized. What does that mean?

Consider a source of EM waves borrowed from PH2223: basically two antenna connected to an AC voltage:

The orientation of the (vector) electric field is taken to be the POLARIZATION of the wave

A hot filament would emit infrared EM waves (aka heat) where each photon has a random orientation and the overall 'wave' contains all orientations and is called UNPOLARIZED (left figure)
A radio antenna emits EM waves where all the photons have the same orientation and is therefore called POLARIZED (right figure).

Mechanical Waves Passing Through a Slit

Polarizing Filters (polaroids)

Like mechanical transverse waves, the orientation (polarization) of EM waves can affect how they interact with matter.
Edwin Land (1929) experimented with thin films of materials with long molecular chains making up the material.
If an EM wave with it's E oriented in the same direction as these molecules tries to pass through this film, much of the energy in the wave gets absorbed by these long molecules.
If the E of the wave is oriented perpendicular to these long molecules, it tends to pass through the material.
These materials were called polaroid sheets.

What if completely unpolarized light strikes a polaroid filter? Unpolarized light means we have light that has E oriented in all possible directions, and each of these will be reduced by the squared cosine of it's angle relative to the filter, so the net effect if we sum over all possible orientations will be the average of cos² which is 1/2.

Two polarizing filters oriented at 90^o to one another:

Three polarizing filters:

Suppose we have three polaroid filters lined up as shown in the figure, with unpolarized light (say from the Sun) entering from the left.

• Filter 1 : what does this filter do?
• Filter 2 : what does this filter do?
• Filter 3 : what does this filter do?

What would happen if we swapped the 2nd and 3rd filters?

Polarization by Reflection

Light reflecting off an interface tends to be polarized. The figure shows unpolarized light striking an interface. The reflected light tends to have it's vector E oriented in and out of the page, and the light transmitted into the material has it's vector E oriented in the plane of the page.

This effect is maximized at a particular angle called the Brewster Angle, which occurs when the reflected and refracted rays make a 90 degree angle with each other.

Brewster Angle:
\[ \tan{\theta_p} = n_2 / n_1 \]

Example: Sunlight reflecting off water
Light from the Sun is unpolarized, so what would be the polarizing angle for sunlight reflecting off water?
This glare coming off the water can be annoying.
How can we eliminate it?

The good:

The bad:

LCD screens are polarized.
(LED-based screens are apparently not.)

Thin Film (Summary)
Reflected Ray : Ray reflecting off an interface: • picks up a sign flip if reflecting off a higher 'n' material • no sign change if reflecting off a lower 'n' material Transmitted Ray : Ray passing through an interface: • no sign change, no matter what the 'n' values are Wavelength Changes while the photon is in the 'film' • λ_film = λ_o/n_film IF THE REFLECTED RAYS HAVE THE SAME SIGN: \[ 2t = (m)\lambda_{film} \hspace{3em} (constructive) \] \[ 2t = (m+\frac{1}{2})\lambda_{film} \hspace{3em} (destructive) \] IF THE REFLECTED RAYS HAVE OPPOSITE SIGNS: \[ 2t = (m+\frac{1}{2})\lambda_{film} \hspace{3em} (constructive) \] \[ 2t = (m)\lambda_{film} \hspace{3em} (destructive) \] Which equation to use depends on BOTH: • What is the film doing to the light? • What do we want/need to happen to this light? (Equally important!)
Lens Coating
Example (from Test 3 practice problems) : A lens (made of glass with n=1.56) has a thin coating applied to it (the coating has an index of refraction of n=1.25). When white light reflects off the lens it appears greenish-yellow (λ = 570 nm) in color. How thick is the coating on the lens? (Give the thinnest two possible thicknesses it might be.) (Be sure to draw a diagram showing any sign-flip(s) involved here and be sure to explain how/why you decided to use the equation you chose to analyze this problem.)
Phone Screen Protector
Suppose we put this same film on our phone. What effect would it have? (The light source is coming from the phone screen itself now, passing through the glass, then hitting the film and then finally reaching our eyes.) What colors (coming from the screen) would we see as extra bright or dim? First Though : What equations would apply here? What equation would yield constructive interference for the light heading towards our eyes? That seems like a pretty negative side effect of adding a screen protector to the phone. Why do we not see this effect? Actual (plastic) screen protector thickness: 0.1 mm Actual (glass) screen protector thickness: 0.3 mm to 0.5 mm How many wavelengths does that represent?

POLARIZATION
Light (or any EM wave) can be polarized. What does that mean? Consider a source of EM waves borrowed from PH2223: basically two antenna connected to an AC voltage:



The orientation of the (vector) electric field is taken to be the POLARIZATION of the wave A hot filament would emit infrared EM waves (aka heat) where each photon has a random orientation and the overall 'wave' contains all orientations and is called UNPOLARIZED (left figure) A radio antenna emits EM waves where all the photons have the same orientation and is therefore called POLARIZED (right figure).

Mechanical Waves Passing Through a Slit

Polarizing Filters (polaroids)
Like mechanical transverse waves, the orientation (polarization) of EM waves can affect how they interact with matter. Edwin Land (1929) experimented with thin films of materials with long molecular chains making up the material. If an EM wave with it's E oriented in the same direction as these molecules tries to pass through this film, much of the energy in the wave gets absorbed by these long molecules. If the E of the wave is oriented perpendicular to these long molecules, it tends to pass through the material. These materials were called polaroid sheets.
What if completely unpolarized light strikes a polaroid filter? Unpolarized light means we have light that has E oriented in all possible directions, and each of these will be reduced by the squared cosine of it's angle relative to the filter, so the net effect if we sum over all possible orientations will be the average of cos² which is 1/2.
Two polarizing filters oriented at 90^o to one another:
Three polarizing filters: Suppose we have three polaroid filters lined up as shown in the figure, with unpolarized light (say from the Sun) entering from the left. • Filter 1 : what does this filter do? • Filter 2 : what does this filter do? • Filter 3 : what does this filter do? What would happen if we swapped the 2nd and 3rd filters?