Monochromatic light with a wavelength of 384 nm passes through a single slit and falls on a screen 86 cm away. if the distance of the first-order dark band is 0.22 cm from the center of the pattern, what is the width of the slit? answer in units of cm.

This is a Fraunhofer single slit experiment, where the light passing through the slit produces an interference pattern on the screen, and where the dark bands (minima of diffraction) are located at a distance of

from the center of the pattern. In the formula, m is the order of the minimum, the wavelenght, the distance of the screen from the slit and the width of the slit.

In our problem, the distance of the first-order band (m=1) is . The distance of the screen is D=86 cm while the wavelength is . Using these data and re-arranging the formula, we can find a, the width of the slit:

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