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In a diffraction pattern due to a single...

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

A

`sin^(-1) ((2)/(3))`

B

`sin^(-1) ((1)/(2))`

C

`sin^(-1)((3)/(4))`

D

`sin^(-1) ((1)/(4))`

Text Solution

Verified by Experts

For first minimum, `sin30^(@) = (lambda)/(a) or, (lambda)/(a) = (1)/(2)`
For n th secondary maximum, a` sin theta = (2n + 1) (lambda)/(2)`
For first secondary maximum, `sintheta = (3lambda)/(2a) = (3)/(2) xx(1)/(2)`
or, `sintheta = (3)/(4) or,theta = sin^(-1) ((3)/(4))`
The option (C) is correct.
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