Subject: Applied Physics 2

Topic: Interference And Diffraction

Difficulty: Medium

Light is incident normally on a grating 0.5 cm wide with 5000 lines. The $\lambda$ s are 5890.2 & 5896.4 $\mathring{A}$. Would you expect these lines to be distinguished by the grating in the $1^{st}$ order?

Width = 0.5 cm, N = 5000 lines /cm

Therefore total number of lines on grating is $\frac{5000}{0.5} = 10000 $

Mean wavelength λ is $\frac{ 5890.2 + 5896.4}{2} = 5893.3 \ A° $

Smallest difference between them is 5896.4 – 5890.2 =6.2 A°

$ RP = \frac{λ}{dλ} = \frac{5893.3}{6.2} = 950.5 $

Also RP= nN

In the first order RP = 1x 10000= 10000

The grating will be able to distinguish the wavelengths 5890.2 & 5896.4 Å

As the required RP is 950.5 and RP in first order is 10000