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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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Knowledge Check

  • In a single slit experiment, angular width of the first minimum obtained by using the light of wavelength 6980 Å is 2^(@) . The width of the slit is

    A
    `2 xx 10^(-5)`mm
    B
    0.02 mm
    C
    0.2 mm
    D
    2 mm

  • In a single slit Fraunhofer diffraction experiment, the wavelength of the light used is 400 mm and the first minimum is obtained for diffraction angle 30^(@) . The magnitude of theta for first secondary maximum is

    A
    `sin^(-1) ((2)/(3))`
    B
    `sin^(-1)((3)/(4))`
    C
    `sin^(-1)((1)/(4))`
    D
    `tan^(-1)((2)/(3))`

  • A slit of width a is illuminated by red light of wavelength 650 nm. The first diffraction minimum is observed at an angle theta_(1) = 5.2^(@) from the direction of the incident beam. The angle theta_(2) at which the second minimum is observed is

    A
    `10.4^(@)`
    B
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    C
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    D
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