First slide

Diffraction

Question

A parallel beam of monochromatic light of wave-length 450 nm passes through a slit of width 0.2 mm. Find the angular divergence in which most of the light is diffracted

Moderate

A

$3 .2 \times 10^{- 4} rad$
B

$5 .4 \times 10^{- 2} rad$
C

$6 .5 \times 10^{- 3} rad$
D

$4 .5 \times 10^{- 3} rad$

Solution

Most of the light is diffracted between the two first order minima. These mimima occur at angle given by
$\begin{array}{l} dsinθ = \pm nλ \\ For n = 1, sinθ = \pm \frac{λ}{d} = \pm \frac{450 \times 10^{- 9}}{0 .2 \times 10^{- 3}} = \pm 2 .25 \times 10^{- 3} rad \\ ∴ The angular divergence = 2 \times θ = 2 \times 2 .25 \times 10^{- 3} rad \\ = 4 .5 \times 10^{- 3} rad \end{array}$

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