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

Order(n) = 1
To find: Angle($\theta$)
Solution: Step1 - Calculating the grating constant(d).
As we know,
Grating spacing(d)
Calculating the angle($\theta$).
As we know that, grating condition is given by:
$d\mathrm{sin}\left(\theta \right)=n\lambda$
$\theta ={\mathrm{sin}}^{-1}\left(\frac{n\lambda }{d}\right)={\mathrm{sin}}^{-1}\left(\frac{1×640×{10}^{-9}}{4.8×{10}^{-6}}\right)$
$\theta ={\mathrm{sin}}^{-1}\left(0.1333\right)={7.66}^{\circ }$
Hence, the angle will be (${7.66}^{\circ }$)