A light is incident normally on a grating, which has 2500  lines per centimeter. Compute the enslavement of a spectral line for which the deviation in second order is 15°. (Ans: 518 nm)



Data Given:

N = 2500 L cm⁻¹ = 250000 L m⁻¹

Angle = Î¸ = 15° 

Order of spectrum = m = 2

To Find:


Wavelength = Î» = ?

Solution:


Using the following formula 

d sin Î¸ = m Î»

or 

λ = `\frac {d sin θ}{m}`

where d = `\frac {1}{N}` So,

λ = `\frac {sin θ}{Nm}`

by putting values of m, θ, and N

λ = `\frac {sin 15°}{250000 L m⁻¹ ｘ 2}`

λ = `\frac {0.259}{500000 L m⁻¹ }`

λ = 5.176 ｘ 10⁻⁷ m

or

λ = 517.6 ｘ 10⁻⁹ m

or

λ = 518  nm --------------------Ans.


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