A single-slit diffraction pattern is formed on a distant screen. Assuming the angles involved are small, by what factor will the width of the central bright spot on the screen change if the wavelength of the illuminating light is doubled

Doubling the wavelength of the diffracting doubles the angle of diffraction. So, the width of the central bright spot pattern formed on the screen will also be doubled.

Explanation:

For a single slit diffraction, the path length difference is related to the wavelength of the light leaving the slit onto the screen by

D sin θ = mλ

where D sin θ is the path length of the waves, each.

mλ is the wavelength of the wavelet

where m is the the order of each minimum

m = m = 1,−1,2,−2,3, . . .

The wavelength of each wavelet is always a multiple of the wavelength of the light source, and from the equation, we can see that the angle of diffraction depend on the wavelength of the light. From this we can see that increasing the wavelength of the light increases the angle of diffraction, and hence we can say that doubling the wavelength will double the diffraction angle. Also, the width of the central bright spot of the screen will spread or increase with the angle of diffraction, so doubling the wavelength doubles the central bright spot on the screen.

trig 15.3 cos