Question

A metallic sheet has a large number of slits, 5.0 mm wide and 16 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? (The speed of these EM waves is c = 3.00 × 10 8 m/s.)

Answer 1

`6* 10^(10)\ Hz`

Step-by-step explanation:

d = Slit gap = 5 mm

Slit distance = 16 cm

c = Speed of light =
`3* 10^8\ m/s`

`\lambda` = Wavelength

We have the relation

`dsin\theta=\lambda`

Here,
`\theta=90`

So

`d=\lambda\\\Rightarrow \lambda=5\ mm`

Frequency is given by

`f=(c)/(\lambda)\\\Rightarrow f=(3* 10^8)/(5* 10^(-3))\\\Rightarrow f=6* 10^(10)\ Hz`

The frequency is
`6* 10^(10)\ Hz`