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)

Respuesta :

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

[tex]d\sin\theta=\lambda[/tex]

For maximum, [tex]\sin\thea=1[/tex]

[tex]d=\lambda[/tex]

[tex]\lambda=20 cm=0.2 m[/tex]

We need to calculate the frequency

[tex]f =\dfrac{c}{\lambda}[/tex]

[tex]f=\dfrac{3\times10^{8}}{0.2}[/tex]

[tex]f=1.5\times10^{9}\ Hz[/tex]

[tex]f=1.5 GHz[/tex]

Hence, The smallest microwave frequency is 1.5 GHz.

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