A diffraction grating has 300 lines per mm. If light of frequency 4.76 × 10¹⁴ Hz is sent through this grating, at what angle does the first order maximum occur? (c = 3.00 × 10⁸ m/s) A) 56° B) 44° C) 22° D) 11° E) 28°

Question

Quizplus · Accepted Answer

The formula to find the angle of the first order maximum in a diffraction grating is given by
sinθ = mλ/d
where m = 1 (for first order maximum), λ = frequency/wavelength, and d = 1/number of lines per unit length (in this case, 1/(300 lines/mm) = 3.33 × 10^(-6) m/mm).
Substituting the given values, we get
sinθ = (1)(4.76 × 10^14 Hz)/(300 lines/mm)(3.00 × 10^8 m/s)
sinθ = 0.042
θ = sin^(-1)(0.042)
θ ≈ 11° (rounded to the nearest degree)

Therefore, the best choice is D.

A Diffraction Grating Has 300 Lines Per Mm