A metallic sheet has a large number of parallel slits,5.0 mm wide and 20 cm apart.This sheet is used as a 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?

Question

Quizplus · Accepted Answer

The slit spacing is given as 20 cm which is equivalent to 200 mm.

We know that for a grating, the condition for maxima is given as:

d sinθ = mλ

where d is the distance between the slits, θ is the angle between the incident beam and the normal to the grating, m is the order of the maxima and λ is the wavelength of the light.

In this case, the incident beam is normal to the grating, so sinθ = 0.

The condition for maxima reduces to:

d = mλ

We are told that the intensity maxima occur 2.0° apart in the central region. This means that the angle between successive maxima is:

θ = 2.0° = 0.035 radians

Since the incident beam is normal to the grating, this angle is also the angle between the diffracted beams.

For the first order maxima (m = 1), the slit spacing should be equal to the wavelength of the microwaves.

Thus,

λ = d/m

Substituting d = 200 mm and m = 1, we get:

λ = 200 mm/1 = 200 mm = 20 cm = 7.0 mm

Therefore, the wavelength of the microwaves is 7.0 mm which corresponds to choice C.

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