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Physics 2054C. Chapter 24 – Wave Nature of Light Interference & Diffraction . Sources. Interference - 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. Constructive Interference.

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physics 2054c

Physics 2054C

Chapter 24 – Wave Nature of Light

Interference & Diffraction

Larry Dennis

interference causes
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
Constructive Interference

Light

Source

Viewing

Screen

D

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

Larry Dennis

destructive interference
Destructive Interference

Viewing

Screen

Light

Source

D

Condition for minimum light intensity is:

Dsin = (n+½), n =0, 1, 2, …

Larry Dennis

interference pattern
n = 0

n = 1

Interference Pattern

Maxima:

Dsin = n

Minima:

Dsin = (n+½ )

Larry Dennis

diffraction properties
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

thin film
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

example
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

example11
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 2m ).
  • This results in destructive interference when it is an odd integer multiple of  ( or 2(m+½) ).

Larry Dennis

example12
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/ +  = 2m  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
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
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
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
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

example two polarizers17
Example: Two polarizers
  • Iout = ½ Iincos2()
    • 0° ½ intensity
    • 90°  no light out

Larry Dennis

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