A grating is just able to resolve 2 lines of $\lambda$ s 5140.34 & 5140.85 $\mathring{A}$ in the $1^{st}$ order. Will it resolve the lines 8037.2 & 8037.5 $\mathring{A}$ in the $2^{nd}$ order?

Subject: Applied Physics 2

Topic: Interference And Diffraction

Difficulty: Medium

RP = $\frac{λ}{dλ}$ = nN

For wavelengths 5140.34 & 5140.85 Å……..

Mean wavelength λ is $\frac{5140.34 + 5140.85}{2} = 5140.595 \ A° $

Smallest difference between them is 5140.85 – 5140.34 = 0.51 A°

First order, n=1

$ N= \frac{1}{n} \times \frac{λ}{dλ} = \frac{1}{1} \times \frac{5140.595}{0.51} = 10080 $

The RP $\frac{λ}{dλ}$ of a grating in second oder should be nN = 2x10080 = 20160

In this case λ is $\frac{8037.20 + 8037.50}{2} = 8037.35 \ A° $

Smallest difference between them is 8037.20 - 8037.50 = 0.30 A°

RP = $\frac{8037.35}{0.30}$ = 26791.17

So the grating will not be able to resolve the lines 8037.20 & 8037.5 AU in second order because the required RP is 26791 is greater than actual RP is 20160.