Light is incident normally on a grating that has 250 lines/mm. Find the wavelength of the spectral line for which the deviation in second order is 12°  (λ = 4158 x 10⁻¹⁰ m) 




Given:

Length of the grating = 1 mm = 1 ｘ 10⁻³ m

Numbers of line = 250 = 2.5 ｘ 10² lines

So, grating element = d = `\frac {1 ｘ 10⁻³}{2.5 ｘ 10²}` m/lines = 4.0 ｘ 10⁻⁶ m/lines


Angle = θ = 12° 

Order of spectral line = m = 2

To Find:


Wavelength = λ = ?

Solution:


Using Braggs Equation

d sin θ = m λ

or 

λ = `\frac {d sin θ}{m}`

by putting values of m, θ, and d

λ = `\frac {4.0 ｘ 10⁻⁶ m ｘ sin 12°}{2}`

λ = `\frac {4.0 ｘ 10⁻⁶ｘ 0.208}{2}` m

by simplifying

λ = `\frac {2 ｘ 0.206}{4.0 ｘ 10⁻⁶}` m

λ = 0.4158 ｘ 10⁻⁶ m

or

λ = 4158 ｘ 10⁻¹⁰ m  -------------------Ans

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