When violet light of wavelength 415 nm falls on a single slit, it creates a central diffraction peak that is 9.90 cm wide on a screen that is 2.53 m away. how wide is the slit?

In the single-slit experiment, the displacement of the minima of the diffraction pattern on the screen is given by
 (1)
where
n is the order of the minimum
y is the displacement of the nth-minimum from the center of the diffraction pattern
 is the light's wavelength
D is the distance of the screen from the slit
a is the width of the slit
The width of the first peak (let's call it ) corresponds to twice the distance of the first minimum: 

which means
 

The wavelength of the light in the problem is 

and the distance of the screen from the slit is


So by using these data and re-arranging the equation, we can find the width of the slit: