A diffraction grating has 5000 lines per centimeter. At what angle does the second-order spectrum of the sodium yellow light of wavelength 589 nm occur? (0.36) 



Given:

Length of the grating = 1 cm = 1 ï½˜ 10⁻² m

Numbers of line = 500 = 5 ï½˜ 10² lines

So, grating element = d = `\frac {1 ｘ 10⁻²}{5 ｘ 10²}` m/lines = 2 ｘ 10⁻⁵ m/lines


Wavelength of light = λ = 589 nm = 589 ｘ 10⁻⁹ m

Order of spectrum = m = 2

To Find:


Angle = θ = ?

Solution:


Using Braggs Equation

d sin θ = m λ

or 

θ = `\sin^{-1} ({mλ}/d)`

by putting values of m, λ, and d

θ = `\sin^{-1} ({2 ｘ589 ｘ 10⁻⁹}/{2 ｘ 10⁻⁵})`

θ = `\sin^{-1} (182.635 ｘ 10⁻⁹⁺⁵)`

θ = `\sin^{-1} (589 ｘ 10⁻⁴)`

θ = 0.36.086°

θ = 0.36° -------------------Ans


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