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SourcesInterference - Causes

- Two waves traveling slightly different distances to get to the same point
- Light shining on one or more openings
- Light reflected from two surfaces

Larry Dennis

Constructive Interference

Light

Source

Viewing

Screen

D

Condition for maximum light intensity isDsin = n, n =0, 1, 2, …

Larry Dennis

Destructive Interference

Viewing

Screen

Light

Source

D

Condition for minimum light intensity is:

Dsin = (n+½), n =0, 1, 2, …

Larry Dennis

Diffraction Properties

- Pattern produced by a single source due to its finite size.
- Important when the source size is comparable to the wavelength.
- Minima: dsin = m, m = 1,2,3 …

Larry Dennis

Diffraction + Interference

Larry Dennis

Thin Film

- Phase changes due to different distances traveled.
- Phase changes due to reflections
- When light moving in a medium of low index of refraction is reflected from a medium of higher index of refraction the reflected waves undergoes a phase change of 180°.

Larry Dennis

1

2

glass, n = 1.44

glass, n = 1.44

Example- How thick (minimum) should the air layer be between two flat glass surfaces if the glass is to appear bright when 480 nm light is incident normally?
- How thick (minimum) should the air layer be between these two glass surfaces if the glass is to appear dark?

Larry Dennis

1

2

glass, n = 1.44

glass, n = 1.44

Example- Phase difference between rays 1 and 2 comes from two sources:
- Phase change of in ray 2 at the bottom air/glass surface.
- Additional distance traveled by ray 2. = 2*2nt/
- Net phase difference between ray’s 1 and 2 is:
- = 2*2nt/ +
- This results in constructive interference when it is an integer multiple of 2 ( or 2m ).
- This results in destructive interference when it is an odd integer multiple of ( or 2(m+½) ).

Larry Dennis

1

2

glass, n = 1.44

glass, n = 1.44

Example- We can equate the net phase difference between ray’s 1 and 2 and the conditions for constructive and destructive interference
- For constructive interference:
- = 2*2nt/ + = 2m 2nt/ + ½ = m
- or 2nt/ = m - ½ (NOTE: t must be positive, so m>0)
- For destructive interference:
- = 2*2nt/ + = 2(m+½) 2t/ + ½ = (m+½)
- or 2nt/ = m

Larry Dennis

CAPA 7: Interferometer

D

As the volume fills with gas the wavelength of the light is reduced from to /n. In the process an additional N = 200 waves are squeezed into the volume. The number of waves already in the volume is 2D/ (the volume has an effective length of 2D since the light goes through twice). So:

The change in the number of waves in the volume is:

N = 2Dn/ - 2D/ N = 2D(n-1) n-1 = N/2D

Note that this differs from the formula discussed in class.

Larry Dennis

Polarization

- Light is an electromagnetic wave.
- Electric field determines the direction of lights polarization.
- Normally, the direction of the electric field points randomly in all directions.
- For polarized light, the electric field vector of all the photons point in the same direction.

Larry Dennis

Polarizers

- Materials that transmit light polarized in a particular direction (along the axis of polarization).
- Transmitted light Iout = Iincos2().

Transmission Axis

Can be in any direction.

Outgoing light is reduced intensity and polarized along the transmission axis.

Larry Dennis

Example: Two polarizers

- Unpolarized light goes into 1st Polarizer:
- Polarized light comes out along transmission axis.
- Intensity is ½ of what went in.
- Polarized light goes into second polarizer:
- Polarized light comes out along transmission axis of 2nd polarizer.
- Intensity reduced by an additional factor of cos2() of the angle between the two transmission axes.

Larry Dennis

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