When a diffraction grating having 5000 lines/cmis illuminated by monochromatic light,the angle between the central maximum and the fourth order maximum is 47.2°.What is the wavelength of the light?
A)138 nm
B)183 nm
C)367 nm
D)637 nm

Question

Quizplus · Accepted Answer

We can use the formula for diffraction grating to find the wavelength of the light:

mλ = d sinθ

where m is the order of the maximum, λ is the wavelength of the light, d is the distance between the grating lines (d = 1/5000 cm), and θ is the angle between the central maximum and the mth maximum.

For the fourth order maximum, m = 4 and θ = 47.2°. Substituting these values into the formula, we get:

4λ = (1/5000) sin 47.2°

Solving for λ, we get:

λ = (1/5000) sin 47.2°/4

λ ≈ 367 nm

When a Diffraction Grating Having 5000 Lines/cmis Illuminated by Monochromatic