Light incident on a pair of slits produces an interference...

Light incident on a pair of slits produces an interference pattern on a screen $2.50 \mathrm{~m}$ from the slits. If the slit separation is $0.0150 \mathrm{~cm}$ and the distance between adjacent bright fringes in the pattern is $0.760 \mathrm{~cm}$, what is the wavelength of the light? [Hint: Is the small angle approximation justified?]

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Key Concepts

Double-Slit Interference

This concept involves the phenomenon where coherent light passes through two closely spaced slits and produces an interference pattern of bright and dark fringes on a screen. The pattern arises from the constructive and destructive interference of the light waves emanating from each slit, which is mathematically expressed through the relationship between the path difference of the waves and their wavelength.

Small-Angle Approximation

In many interference experiments, the angles involved are very small, allowing the use of the small-angle approximation where sin(?) and tan(?) are approximately equal to ? when measured in radians. This simplification facilitates easier calculation of fringe positions while introducing negligible error for small values of ?.

Fringe Spacing

Fringe spacing refers to the distance between consecutive bright (or dark) fringes on an interference pattern. It is directly related to the wavelength of light, the separation of the slits, and the distance from the slits to the observation screen. This relationship underpins the measurement techniques used to determine the wavelength of light in interference experiments.

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