Question

If a light is incident on a grating with 5000 lines/cm, then the angular separation of the two lines (5000 Å and 5006 Å) in first order spectrum is ______

(a) 0.01°

(b) 0.02°

(c) 0.03°

(d) 0.04°

I had been asked this question in a national level competition.

I'd like to ask this question from Resolving Power of Grating in division Diffraction of Engineering Physics II

Answer 1

Right answer is (b) 0.02°

Easy explanation: Here, N = 5000. Therefore, a + b = 1/5000 cm

Now we know, (a + b) sinΘ = nλ

For λ = 5000 Å, sinΘ1 = 5 X 10^-5 X 5000

Θ1 = 14.47°

For λ = 5006 Å, sinΘ2 = 5.006 X 10^-5 X 5000

Θ2 = 14.49°

Angular separation = Θ2 – Θ1 = 0.02°.