7. Intereference – explanation and formulas for constructive and destructive interference, interference in thin films, double slit interference. (4p.)

Question 1

Intereference – explanation and formulas for constructive and destructive interference

Answer 1

An effect caused by identical waves from two sources that overlap at a point of space making a combined wave intensity greater (constructive interference) or smaller (destructive interference) than the intensity of either of two waves.

Question 2

Interference in thin films

Answer 2

Light bands correspond to regions at which constructive interference is occurring between the reflected waves and dark bands correspond to destructive interference regions. As the thickness of the film varies from one location to another, the interference may change from constructive to destructive.

Thin-film interference is a natural phenomenon in which light waves reflected by the upper and lower boundaries of a thin film interfere with one another, either enhancing or reducing the reflected light. When the thickness of the film is an odd multiple of ¼ wavelength of the light on it, the reflected waves from both surfaces interfere to cancel each other. Since the wave cannot be reflected, it is completely transmitted instead. When the thickness is a multiple of ½ wavelength of the light, the two reflected waves reinforce each other, increasing the reflection and reducing the transmission.

Question 3

Double slit interference

Answer 3

Young carried out an experiment in which the wave nature of light was demonstrated. The bright bands correspond to interference maxima and the dark band interference minima.

Interference maxima for:
dsin(θ) = mλ, m =0, 1, 2…

Interference minima for:
dsin(θ) = (m+1/2)λ, m =0, 1, 2…

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