First slide

Diffraction of light-Wave Optics

Question

Plane microwaves are incident on a slit of width 5.0 cm, if first diffraction minimum is formed at an angle $θ = 30^{\circ}$ , then what is the wavelength of the microwaves?

Moderate

A

5 cm
B

2.5 cm
C

1.25 cm
D

10 cm

Solution

Given
Width of the slit $b = 5.0 cm$
First diffraction minimum is formed at $θ = 30^{\circ}$
For the diffraction minima,
We have $b \sin θ = n λ$
$\Rightarrow \sin θ = \frac{λ}{b}$
For the first minima, we put n=1
$\begin{array}{l} \Rightarrow \sin 30 = \frac{λ}{5} \\ \Rightarrow \frac{λ}{5} = \frac{1}{2} \\ \Rightarrow λ = \frac{5}{2} = 2.5 cm \end{array}$

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