Wave Optics

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A third mirror is partially reflecting

Called a beam splitter

The incident light hits the beam splitter and is divided into two waves

The waves reflect from the mirrors at the top and right and recombine at the beam splitter

Slide 7

After being reflected again from the beam splitter, portions of the waves combine at the detector

The only difference between the two waves is that they travel different distances between their respective mirrors and the beam splitter

The path length difference is ΔL = 2L2 – 2L1

The path length difference is related to the wavelength of the light

If N is an integer, the two waves are in phase and produce constructive interference

If N is a half-integer the waves will produce destructive interference

Slide 8

For constructive interference, ΔL = m λ

For destructive interference, ΔL = (m + ½) λ

m is an integer in both cases

If the interference is constructive, the light intensity at the detector is large

Called a bright fringe

If the interference is destructive, the light intensity at the detector is zero

Called a dark fringe

Slide 9

Example

A helium–neon (He–Ne) laser emits light with a wavelength of approximately λHe–Ne =633 nm. Suppose this light source is used in a Michelson interferometer and one of the mirrors is moved a distance d such that exactly N = 1,000,000 bright fringes are counted, calculate d.

Solution:

When the mirror moves a distance d, the distance traveled by the light changes by 2d because the light travels back and forth between the beam splitter and the mirror.

d = 0.5×1000000×633×10-9m=0.317m

ΔL=2L2 – 2L1=2(L2 – L1)=2d

Slide 10

Thin-Film Interference

Assume a thin soap film rests on a flat glass surface

The upper surface of the soap film is similar to the beam splitter in the interferometer

It reflects part of the incoming light and allows the rest to be transmitted into the soap layer after refraction at the air-soap interface

Slide 11

The transmitted ray is partially reflected at the bottom surface

The two outgoing rays meet the conditions for interference

They travel through different regions

They recombine when they leave the film

They are coherent because they originated from the same source and initial ray

From the speed of the wave inside the film

The wavelength changes as the light wave travels from a vacuum into the film

The number of extra wavelengths is