Young's double-slit experiment is performed with 589 -nm...

Young's double-slit experiment is performed with 589 -nm light and a distance of $2.00 \mathrm{m}$ between the slits and the screen. The tenth interference minimum is observed $7.26 \mathrm{mm}$ from the central maximum. Determine the spacing of the slits.

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Key Concepts

Young's Double-Slit Experiment

This experiment demonstrates the interference of light waves, where light passes through two closely spaced slits and produces an interference pattern of bright and dark fringes on a screen. It is fundamental in illustrating the wave nature of light and the principle of superposition.

Destructive Interference and Minima

Dark fringes (minima) in the interference pattern result from destructive interference, which occurs when the path difference between the two waves equals an odd multiple of half a wavelength. This condition can be mathematically expressed, for small angles, to relate the position of the minima to experimental parameters such as wavelength, slit spacing, and distance to the screen.

Small Angle Approximation

In many interference experiments, including the double-slit setup, the distance between the slits and the screen is much larger than the fringe spacing, making the angles involved small. The small angle approximation (where sin? and tan? are approximately equal to ? in radians) simplifies the relationship between fringe position and the experimental geometry, allowing for straightforward calculations.

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