Subject: Applied Physics 2

Topic: Interference And Diffraction

Difficulty: Medium

Let the line of unknown wavelength λ$_1$ in the order n$_1$ coincides with the line of known wavelength λ in the n$^{th}$ order provided.

(a+b) sinθ = nλ = n$_1$ λ$_1$

$ λ_1 = \frac{nλ}{n_1} $

Given for n= 4 , λ = 5000 A° and λ$_1$ lies in the range 4000 – 7000 Å

$ λ_1 = \frac{4x5000}{n_1} = \frac{20000 }{n_1} $

so, If n$_1$ = 3, $ λ_1 = \frac{20000}{3} = 6666.6 \ A° $

If n$_1$ = 2, $ λ_1 = \frac{20000}{2} = 10000 \ A° $

If n$_1$ = 1, $ λ_1 = \frac{20000}{1} = 20000 \ A° $

So, in the grating spectrum the spectrum the spectral lines with wavelengths 6666.6 A° in the range 4000 – 7000 Å ,will coincide with fourth order line of 5000A°