Question

A diffraction grating has 4000 lines/cm. The dispersive power of the grating in the third order spectrum in the wavelength region of 5000 Å is _____________

(a) 5000

(b) 10000

(c) 15000

(d) 20000

I have been asked this question in class test.

This interesting question is from Plane Diffraction Grating topic in portion Diffraction of Engineering Physics II

Answer 1

Correct option is (c) 15000

Easy explanation: We know; the dispersive power of a grating is given by:

\(\frac{\partial \theta}{\partial \lambda}\) = n/(a + b) cosθ

Now, here n = 3 and a + b = 1/5000 cm

Here, sinθ = nλ/(a + b) = 0.6

cosθ = 0.8

Now, \(\frac{\partial \theta}{\partial \lambda}\) = 3 X 4000/0.8

= 15000.