Question

Mercury light is normally incident on a grating . The diffraction angle in the first order spectrum from a green spectral line of wavelength 5460 A is 20. Find the number of lines per cm of grating

Answer 1

Solution:

In this case,

• n = 1

• A diffraction grating diffracts light at 20⁰

Given:

θ = 20⁰;

λ = 5460 A⁰

N =?

• Using formula, n λ = d sinθ ... (putting n=1)

N =1000 limes per mm length.

So, d =1/N ... (Where, N is th enumber of lines per m length).

⇒ λ = sinθ/N

⇒ N = sinθ/λ

⇒ N = sin20/(5460×10^-10) ... (sin20 ≅ 0.34)

⇒ N = (0.34/5460)×(10^10) = 0.00006227×10¹⁰ = 622700 per m

• Per cm = 622700/100 = 6227

Final answer:

The number of lines per cm of the grating is 6227.

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