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Q.

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:

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a

$\sin^{- 1} (\frac{1}{2})$

b

$\sin^{- 1} (\frac{1}{4})$

c

$\sin^{- 1} (\frac{3}{4})$

d

$\sin^{- 1} (\frac{2}{3})$

answer is B.

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Detailed Solution

detailed_solution_thumbnail

In diffraction single slit experiment condition for n^th dark band,
$a. \sin 30 = n λ \dots (1)$
Condition for bright band
$a \sin θ = (2 n + 1) \frac{λ}{2} \dots (2)$
Where ‘a’ is slit width and
$λ$ is wavelength.
Divide (2) by (1) $= \sin θ = \frac{3}{4} .$

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