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Two parallel beams of light P and Q (sep...

Two parallel beams of light P and Q (separation d) containing radiation of wavelengths `4000A` and `5000A` (which are mutually coherent in each wavelength separately) are incident normally on a prism as shown in fig. The refractive index of the prism as a function of wavelength is given by the relation. `mu(lamda)=1.20+(b)/(lamda^(2))` Where `lamda` is in `A` and b is positive constant. The value of b is such that the condition wave length and is not satisfied for the other.
(a) Find the value of b.
(b) find the deviation of the beams transmitted through the face AC. (c) A convergent lens is used to bring these transmitted beams into focus. If the intensities of transmission form the face AC, are 41 and I respectively, find the resultant intensity at the focus. `

Text Solution

Verified by Experts

The correct Answer is:
9 I
Values of `mu,alpha` etc. are given because there `2` more parts asked in actual `JEE` paper based on value of `'b'` and `delta.` But for finding the intensity, we don't need any of this.
The paths of `2` rays is as show. Clearly the path difference between them is.
`PQ-muRS`
`=(PS) cos (90-r) - mu.d tantheta`
`=(PS) sin r-mu d tantheta`.
Now , by snells. lwa.
`mu sintheta=1. sin r. and PS=(d)/(cos theta)`
we get path difference `=(d mu sin theta)/(cos theta) -mu d tantheta=0`.
Hence the intensity is maximum at `9I`.
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Two parallel beams of light P and Q (separation d) containing radiations of wavelengts 4000Å and 5000 Å (which are mutually coherent in each wavelength separately) are incident normally on a prism as shown in figure the refractive index of the prism as a function of wavelength is given by the relation mu(lamda)=1.20+(b)/(lamda^(2)) where lamda is in Å and b is a positive constant. The value of b is such that the condition for total reflection at the face AC is just satisfied for one wavelength and is not satisfied for the other. A convergent lens is used to bring these transmitted beams into focus. If the intensities of the upper and the lower beams immediately after transmission from the face AC, are 4I and I respectively, find the resultant intensity at the focus.

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Knowledge Check

  • The energy of a photon of wavelength lamda is given by

    A
    `hlamda`
    B
    `ch lamda`
    C
    `lamda//hc`
    D
    `hc//lamda`

  • The refractive index of a medium is given by mu=A+(B)/(lambda^(2)) where A and B are constants and lambda is the wavelength of light. Then the dimensions of B are the same as that of

    A
    Wavelength
    B
    Area
    C
    Volume
    D
    Velocity

  • When light of wavelength lambda on an equilateral prism, kept on its minimum deviation position, it is found that the angle of deviation equals the angle the angle of the prism itself. The refractive index of the material of the prism for the wavelength lambda is

    A
    `sqrt3`
    B
    `sqrt(3//2)`
    C
    `2`
    D
    `sqrt2`