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A diffraction grating is ruled with 600 ...

A diffraction grating is ruled with 600 lines per millimetre. When monochromatic light falls normally on the grating, the first order diffracted beams are observed on the far side of the grating each making an angle of `15^@` with the normal to the grating.
What is the frequency of the light?

A

(a) `1.2xx10^(13)Hz`

B

(b) `4.7xx10^(13)Hz`

C

(c) `1.9xx10^(14)Hz`

D

(d) `7.0xx10^(14)Hz`

Text Solution

Verified by Experts

The correct Answer is:
D
The angle of diffraction `theta_n` for nth order diffraction pattern of the light is given by
`dsin theta_n=nlambda`
where d=spacing between adjacent slits in diffraction grating `=10^-1/600m`
n=1 for first-order diffracted beam.
`theta_1=15^@`
`implies(dsintheta_1)/(1)=(10^-3)/(600)sin15^@=4.3xx10^-7m`
Thus frequency of light,
`f=c/lambda=(3xx10^8)/(4.3xx10^-7)=7.0xx10^(14)Hz`.
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Knowledge Check

  • In a spectrometer experiment, monochromatic light is incident normally on a diffraction grating having 4.5xx10^5 lines per metre. The seond order line is seen at an angle of 30^@ to the normal. What is the wavelength of the light?

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    B
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    C
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    D
    (d) `589nm`

  • A beam of monochromatic light of wavelength lambda falls normally on a diffraction grating of line spacing d. If theta is the angle between the second-order diffracted beam and the direction of the incident light, what is the value of sin theta ?

    A
    `(lambda)/(d)`
    B
    `(d)/(lambda)`
    C
    `(2 lambda)/(d)`
    D
    `(2d)/(lambda)`

  • Light is incident normally on a diffraction grating through which the first order diffraction is seen at 32^@ . The second order diffraction will be seen at

    A
    (a) `48^@`
    B
    (b) `64^@`
    C
    (c) `80^@`
    D
    (d) There is no second order diffraction in this case.

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