Red light of wavelength 600.0 nm is incident on a grating. If the separation between the slits is 5.0 × 10^-⁵ m, at what angle does the first principal maximum occur? A)0.6 × 10^-²rad B)0.8 × 10^-²rad C)1.2 × 10^-²rad D)3.6 × 10^-²rad E)5.0 × 10^-²rad

Question

Quizplus · Accepted Answer

The formula for the angle of diffraction of a grating is given by:
$sin θ = \frac{mλ}{d}$
where m is the order of diffraction, λ is the wavelength of light, and d is the separation between the slits.
For the first principal maximum, m = 1. Substituting the given values, we get:
$sin θ = \frac{1 × 600.0 × 10^{-9} m}{5.0 × 10^{-6} m} = 0.12$
Taking the inverse sine of both sides, we get:
$θ = sin^{-1} (0.12) = 1.2 × 10^{-1} rad = 1.2 × 10^{-1} × \frac{180}{\pi}° = 6.9°$
Therefore, the answer is C) 1.2 × 10^-1 rad, or approximately 0.69°.

Red Light of Wavelength 600