A grating has 9600 lines uniformly spaced over a width of 3 cm and is illuminated by light from mercury vapour lamp,find dispersion in the third order in the vicinity of green lines of wave length 5460A°.
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Given info : A grating has 9600 lines uniformly spaced over a width of 3 cm and is illuminated by light from mercury vapour lamp.
To find : The dispersion in the 3rd order in the vicinity of green lines of wavelength 5460 A° is ...
solution : N = 9600/3cm = 32 lines per cm
d = separation = 1/N = 1/3200
n = 3 [ ∵ 3rd order ]
λ = wavelength = 5460 A° = 5460 × 10^-8 cm
using formula, sinθ = nλ/d
= 3 × 5460 × 10^-8 × 3200
= 0.52416
⇒θ = 31.6°
so, cosθ = 0.851
now dispersion power in 3rd order = Nn/cosθ
= 3200 × 3/0.851
= 11,280.8461 ≈ 11281
Therefore the dispersion in the 3rd order in the vicinity of green lines is 11281
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