A screen is placed 50.0 cm from a single slit, which is...

A screen is placed $50.0 \mathrm{cm}$ from a single slit, which is illuminated with light of wavelength $690 \mathrm{nm}$. If the distance between the first and third minima in the diffraction pattern is $3.00 \mathrm{mm},$ what is the width of the slit?

Key Concepts

Diffraction Minima

The diffraction minima in a single slit diffraction pattern are determined by the conditions under which the light waves interfere destructively. The positions of the minima are given by the equation a sin? = m?, where 'a' is the slit width, '?' is the angle relative to the central maximum, '?' is the wavelength of light, and 'm' is a nonzero integer representing the order of the minimum. This relation is fundamental in linking the physical dimensions of the slit with the observed pattern.

Small Angle Approximation

When the distance from the slit to the screen is much larger than the size of the diffraction pattern, the small angle approximation can be applied. In this approximation, the angle ? is small enough that sin? and tan? can be approximated by the ratio of the fringe displacement to the distance from the slit to the screen. This simplifies calculations by enabling a direct relationship between the geometry of the pattern and the slit width.

Single Slit Diffraction

Single slit diffraction is a wave phenomenon observed when light encounters a narrow aperture, causing the beam to spread out and form a distinct pattern of bright and dark fringes on a screen. This occurs due to the interference of secondary wavelets emanating from different parts of the same slit, and it demonstrates that light behaves as a wave when it passes through a small opening.

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