Answer to Question #254965 in Optics for Abdul

Question

A diffraction grating, ruled with 300 lines per mm, is illuminated with a white light source at normal incidence.

(i) What is the angular separation, in the third-order spectrum, between the 400 nm and 600 nm lines? [5]

(ii) Water (of refractive index 1.33) now fills the whole space between the grating and the screen?

What is the angular separation, in the first-order spectrum, between the 400 nm and 600 nm lines? [5]

Answer 1

1)

$d\sin \theta=k\lambda,$

$\sin\theta=\frac{k\lambda}d=0.45,$

$\theta=26.7°,$

2)

$d\frac{\sin \theta'}n=m\lambda,$

$\sin\theta'=\frac{mn\lambda}d=0.2,$

$\theta'=11.5°.$