University Physics Volume 3

# Summary

### 3.1Young'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.

### 3.2Mathematics of Interference

• In double-slit diffraction, constructive interference occurs when $dsinθ=mλ(form=0,±1,±2,±3…)dsinθ=mλ(form=0,±1,±2,±3…)$, where d is the distance between the slits, $θθ$ is the angle relative to the incident direction, and m is the order of the interference.
• Destructive interference occurs when $dsinθ=(m+12)λform=0,±1,±2,±3,…dsinθ=(m+12)λform=0,±1,±2,±3,…$.

### 3.3Multiple-Slit Interference

• Interference from multiple slits ($N>2N>2$) 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.

### 3.4Interference 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 $180°180°$ phase change (or a $λ/2λ/2$ 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.

### 3.5The Michelson Interferometer

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