Question

What is the minimum number of lines per cm in a 2.5 cm wide grating spectrum which will just resolve two sodium lines (5890 Å and 5896 Å) in the first order spectrum?

(a) 98

(b) 196

(c) 392

(d) 694

I got this question in an online interview.

The query is from Resolving Power topic in section Optics of Engineering Physics II

Answer 1

The correct answer is (c) 392

The best explanation: Now, we know that for a grating \(\frac{\lambda}{d\lambda}\)=nN

    λmean = 5893 Å = 5.89 X 10^-7m

   dλ = 6 Å = 6 X 10^-10 m

    n = 1, N =?

So, N = \(\frac{\lambda}{nXd\lambda}\) = 982

No of lines per cm = 982/2.5 = 392.