Summary

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Summary

3.1 Young's Double-Slit Interference

Young’s double-slit experiment gave definitive proof of the wave character of light.
An interference pattern is obtained by the superposition of light from two slits.

3.2 Mathematics of Interference

In double-slit diffraction, constructive interference occurs when $d sin θ = m λ (for m = 0, ± 1, ± 2, ± 3 …)$ , where d is the distance between the slits, $θ$ is the angle relative to the incident direction, and m is the order of the interference.
Destructive interference occurs when $d sin θ = (m + \frac{1}{2}) λ for m = 0, ± 1, ± 2, ± 3,…$ .

3.3 Multiple-Slit Interference

Interference from multiple slits ( $N > 2$ ) produces principal as well as secondary maxima.
As the number of slits is increased, the intensity of the principal maxima increases and the width decreases.

3.4 Interference in Thin Films

When light reflects from a medium having an index of refraction greater than that of the medium in which it is traveling, a $180 °$ phase change (or a $λ / 2$ shift) occurs.
Thin-film interference occurs between the light reflected from the top and bottom surfaces of a film. In addition to the path length difference, there can be a phase change.

3.5 The Michelson Interferometer

When the mirror in one arm of the interferometer moves a distance of $λ / 2$ each fringe in the interference pattern moves to the position previously occupied by the adjacent fringe.

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