Subject: Applied Physics 2

Topic: Interference And Diffraction

Difficulty: Medium

The resolving power (RP) of a diffraction grating is given by $\lambda /d\lambda$ = nN. Show that the frequency range that can be resolved is given by dν = $c/nN\lambda$.

RP = $\frac{λ}{dλ}$ = nN

dλ = $\frac{λ}{nN}$

Velocity = frequency x wavelength

C= νλ

$ ν = \frac{c}{λ}$……………………………(1)

Differentiate the equation 1

$ dν = -c \frac{dλ}{λ^2} $………………………………(2)

Substituting equation 1 in equation 2,

$ dν = -c \frac{λ}{nN λ^2} $

Therefore, $ dν = -\frac{c}{nNλ} $

Negative sign shows that if wavelength range is λ + dλ, then frequency range will be ν -Δν .