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

Answer:

The smallest microwave frequency is 1.5 GHz.

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

$f =\dfrac{c}{\lambda}$

$f=\dfrac{3\times10^{8}}{0.2}$

$f=1.5\times10^{9}\ Hz$

$f=1.5 GHz$

Hence, The smallest microwave frequency is 1.5 GHz.