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In the diffraction pattern due to a sing...

In the diffraction pattern due to a single slit of width 'd' with incident light of wavelength `'lamda',` at an angle of diffraction `'theta',` the condition for first minimum is

A

`lamda sin theta =d`

B

`d cos theta= lamda`

C

`d sin theta=lamda`

D

`lamda cos theta=d`

Text Solution

Verified by Experts

The correct Answer is:
C
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(a) Derive the relation asintheta=lamda for the first minimum of the diffraction pattern produced due to a single-slit of width 'a' using light of wavelength lamda . (b) State with reason, how the linear width of central maximum will be affected if (i) monochromatic yellow light is replaced with red light, and (ii) distance between the slit and the screen is increased. (c) using the monochromatic light of same wavelength in the experimental set-up of the diffraction pattern as well as in the interference pattern where the slit separation is 1mm, 10 interference fringes are found to be within the central maximum of the diffraction pattern. determine the width of the single-slit, if the screen is kept at the same distance from the slit in the two cases.

(a) Derive the relation a sin theta=lambda for the first minimum of the diffraction pattern produced due to a single slit of width ‘a’ using light of wavelength lambda . (b) State with reason, how the linear width of central maximum will be affected if (i) monochromatic yellow light is replaced with red light, and (ii) distance between the slit and the screen is increased. (c) Using the monochromatic light of same wavelength in the experimental set-up of the diffraction pattern as well as in the interference pattern where the slit separation is 1 mm, 10 interference fringes are found to be within the central maximum of the diffraction pattern. Determine the width of the single slit, if the screen is kept at the same distance from the slit in the two cases.

Knowledge Check

  • In the diffraction pattern due to single slit, in the direction of theta=0 we get

    A
    first secondary minimum
    B
    central maximum
    C
    first secondary maximum
    D
    second secondary maximum

  • In single slit diffraction pattern :

    A
    Central fringe has negligible width than others
    B
    All fringes are of same width
    C
    Central fringe does not exist
    D
    None of the above

  • In single slit diffraction pattern :

    A
    central fringe has negligible width than others
    B
    all fringes are of some width
    C
    central fringe does not exist
    D
    none of the above

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