A metallic sheet has a large number of parallel slits,5.0 mm wide and 20 cm apart.This sheet is used as a diffraction grating for microwaves.A wide parallel beam of microwaves is incident normally on the sheet.If the intensity maxima occur 2.0° apart in the central region,what is the wavelength of the microwaves?
A)5.0 mm
B)6.0 mm
C)7.0 mm
D)8.0 mm
E)9.0 mm

Question

Quizplus · Accepted Answer

The distance between the slits, d = 20 cm = 0.2 m, and the width of each slit, a = 5.0 mm = 5.0 x 10^-3 m. The angle between the intensity maxima, θ = 2.0° = 2.0 x π/180 radians. The distance between the central maximum and the first-order maximum is given by:
sinθ = λ/d
λ = d sinθ
λ = 0.2 x sin(2.0° x π/180)
λ = 7.02 x 10^-3 m
λ = 7.0 mm (to two significant figures)

Therefore, the wavelength of the microwaves is 7.0 mm and the best choice is C.

A Metallic Sheet Has a Large Number of Parallel Slits,5