Question

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. What is the smallest microwave frequency for which only the central maximum occurs? (c = 3.00 × 108 m/s)

Answer 1

The smallest microwave frequency is 1.5 GHz.

Step-by-step explanation:

Given that,

Distance d= 20 cm

We need to calculate the wavelength

Using formula for maximum diffraction

`d\sin\theta=\lambda`

For maximum,
`\sin\thea=1`

`d=\lambda`

`\lambda=20 cm=0.2 m`

We need to calculate the frequency

`f =(c)/(\lambda)`

`f=(3*10^(8))/(0.2)`

`f=1.5*10^(9)\ Hz`

`f=1.5 GHz`

Hence, The smallest microwave frequency is 1.5 GHz.