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?

Question

Answer 1

Given in question: Number of slits(N) = 2085 lines/cm = 208500 lines/m

Wavelength (λ) = 640 n m = 640 \times 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 \times 10^{- 6} m

Calculating the angle(

θ

).
As we know that, grating condition is given by:

d \sin (θ) = n λ

θ = \sin^{- 1} (\frac{n λ}{d}) = \sin^{- 1} (\frac{1 \times 640 \times 10^{- 9}}{4.8 \times 10^{- 6}})

θ = \sin^{- 1} (0.1333) = {7.66}^{\circ}

Hence, the angle will be (

{7.66}^{\circ}

)

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?

Answers (1)

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