White light is spread out into its spectral components by a diffraction grating. If the grating has 2085 lines per centimeter, at what angle does red light of wavelength 640 nm appear in first-order spectrum?

Ishaan Booker 2022-07-17 Answered
White light is spread out into its spectral components by a diffraction grating. If the grating has 2085 lines per centimeter, at what angle does red light of wavelength 640 nm appear in first-order spectrum?
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Answers (1)

Jorge Franklin
Answered 2022-07-18 Author has 11 answers
Given in question: Number of slits(N) = 2085 lines/cm = 208500 lines/m
Wavelength ( λ ) = 640   n m = 640 × 10 9   m
Order(n) = 1
To find: Angle( θ)
Solution: Step1 - Calculating the grating constant(d).
As we know,
Grating spacing(d) = 1 N = 1208500 = 4.8 × 10 6   m
Calculating the angle( θ).
As we know that, grating condition is given by:
d sin ( θ ) = n λ
θ = sin 1 ( n λ d ) = sin 1 ( 1 × 640 × 10 9 4.8 × 10 6 )
θ = sin 1 ( 0.1333 ) = 7.66
Hence, the angle will be ( 7.66 )
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