First slide

Diffraction

Question

In a diffraction pattern due to a single slit of width $a$ , the first minimum is observed at an angle $30^{0}$ when light of wavelength $5000 Å$ is incident on the slit. The first secondary maximum is observed at an angle of

Moderate

A

$s i n^{- 1} (\frac{1}{2})$
B

$s i n^{- 1} (\frac{3}{4})$
C

$s i n^{- 1} (\frac{1}{4})$
D

$s i n^{- 1} (\frac{2}{3})$

Solution

For first minimum, the path difference between extreme waves, $a \sin θ = λ$
$Here θ = 30 ° \Rightarrow \sin θ = \frac{1}{2} ∴ a = 2 λ . . . . . . . . . . (1)$
For first secondary maximum, the path difference between extreme waves
$a \sin θ^{'} = \frac{3}{2} λ or (2 λ) \sin θ^{'} = \frac{3}{2} λ$ $[Using eqn (i)]$
$or \sin θ^{'} = \frac{3}{4} ∴ θ^{'} = \sin^{- 1} (\frac{3}{4})$

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