Question

A beam of light is incident normally on a diffraction grating of width 1 cm. It is found that at 30° , the n^th order diffraction maximum for λ₁ = 600 Å is super-imposed on the (n+1)^th order for λ₂ = 500 Å. How many lines per cm does the grating have? Find out whether the first order spectrum from such a grating can be used to resolve the wavelengths λ₃ = 5800 Å and λ₄ = 5802 Å ? 

Answer 1

Condition for diffraction maxima is

(b + e)sin θ = nλ

For given two wavelength the maxima condition can be written as

For 1^st order spectrum, the resolving power of the given grating is

R = nN = 20000

Whereas to resolve the wavelengths λ₃ = 5800 Å and λ₄ = 5802 Å the required resolving power is

R = λ/dλ = 5800/2 = 2900.

Resolving power of the given grating  (20000) is more than required(2900) . Thus, given grating will resolve the wavelengths λ₃ = 5800 Å and λ₄ = 5802  Å.