A second order spectrum is formed at an angle of 38° when light falls normally on a diffraction grating having 5400 lines per centimeter. Determine wavelength of the light used. (Ans: 570 nm)



Data Given:


Angle = θ = 38° 

Order of spectrum = m = 2

N = 5400 L cm⁻¹ = 540000 L m⁻¹

To Find:


Wavelength = λ = ?

Solution:


Using the following formula 

d sin θ = m λ

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 38°}{540000 L m⁻¹ｘ 2}`

λ = `\frac {0.616}{1080000 L m⁻¹ }`

λ = 5.704 ｘ 10⁻⁷ m

or

λ = 570.4 ｘ 10⁻⁹ m

or

λ = 570  nm --------------------Ans.


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