Diffraction grating: A metallic sheet has a large number of slits, 5.0 mm wide and 20 cm apart, and is used as a diffraction grating for microwaves. A wide parallel beam of microwaves is incident normally on the sheet. If the microwave wavelength is 6.0 cm, what is the largest angle away from the central maximum at which an intensity maximum occurs.
A) 64°
B) 69°
C) 74°
D) 79°
E) 84°

Question

Quizplus · Accepted Answer

The largest angle away from the central maximum at which an intensity maximum occurs is given by the equation:sin θ = mλ/dwhere m is the order of the maximum, λ is the wavelength of the microwaves, and d is the distance between the slits.For the first-order maximum (m = 1), we have:sin θ = λ/d = 6.0 cm / 20 cm = 0.3θ = sin^-1(0.3) = 17.5°For the second-order maximum (m = 2), we have:sin θ = 2λ/d = 12.0 cm / 20 cm = 0.6θ = sin^-1(0.6) = 36.9°The largest angle away from the central maximum at which an intensity maximum occurs is therefore 36.9°, which is closest to choice A) 64°.

Diffraction Grating: a Metallic Sheet Has a Large Number of Slits