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If two coherent source are placed at a d...

If two coherent source are placed at a distance `3lambda` from each other, symmetric to the centre of the circel as shown in figure, Find thenumber of fringes shown on the screen, placed along the circumference ?

A

16

B

12

C

8

D

4

Text Solution

Verified by Experts

The correct Answer is:
B
Path difference at any point 'P' on the circumference

`Delta x = S_(1)P - S_(2)P S_(1) P = R + (3lambda)/(2)cos theta`
`S_(2)P = R - (3lambda)/(2)cos theta Delta x = S_(1)P - S_(2)P`
`Delta x = 3lambda cos theta` For maxima at 'P'
`Delta x = n lambda = 3lambda cos theta`
`cos theta = (n)/(3) [n = 0,1,2,3,---]`
`cos theta = 0, (1)/(3), (2)/(2), 1` [maximum value of `cos theta = 1`]
`:.` In each quadrant there are 3 maximas. Hence in 4 quadrants there willbe 12 maximas. Hence 12 minima in between so there are 12 fringes
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Knowledge Check

  • Two coherent light sources A and B are at a distance 3lambda from each other (lambda =wavelength)The distances from A on the X-axis at which the interference is constructive are

    A
    `3lambda`
    B
    `8lambda`
    C
    `5lambda//4`
    D
    `8.75 lambda`

  • In a system of two dipoles placed in the way as shown in figure :

    A
    It is possible to consider a spherical surface of radius a and whose centre lies within the square shown through which total flux is `+ ve`
    B
    It is possible to consider a spherical surface of their a and whose centre lies within the square shown through which total flux is `-ve`
    C
    It is possible to consider a spherical surface of radius a and whose centre lies within the square shown through which total flux is zero
    D
    There are two points within the square at which EF is zero.

  • Two coherent light sources S_1 and S_2 (lambda=6000Å) are 1mm apart from each other. The screen is placed at a distance of 25cm from the sources. The width of the fringes on the screen should be

    A
    (a) `0.015cm`
    B
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    C
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    D
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