Question

White light is normally incident on a diffraction grating that has 6500 lines/cm. What is the angular separation Delta theta = theta_R - theta_V between red light (lambda = 700nm) and violet light (lambda = 400nm) in the first order (m = 1)?

Answer 1

First we need to find the Angle , $\theta$ =sin^-1(m $\lambda$ /d)

Where m=1

Wavelength, $\lambda$ =700 nm for red and 400 nm for violet

d=6500 lines /cm

So $\theta$ R=sin^-1(700/6500)=6.18

$\theta$ V=sin^-1(400/6500)=3.52

So the difference in angle is ,d $\theta$ =2.65