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Two identical narrow slits S1 and S2 ar...

Two identical narrow slits `S_1 and S_2` are illuminated by the light of a wavelength`lamda` from a point source P. If , as shown in the diagram above , the light is then allowed to fall on a screen , and if n is a positive integer , the condition for destructive interference at Q is

A

`(l_1-l_2) =(2n+1)lamda//2`

B

`(l_3-l_4) =(2n+1)lamda//2`

C

`(l_1+l_2)-(l_3+l_4) =nlamda`

D

`(l_1+l_3)-(l_2+l_4) =(2n+1)lamda//2`

Text Solution

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The correct Answer is:
D
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Consider the situation shown in figure. The two slits S_1 and S_2 placed symmetrically around the central line are illuminated by a monochromatic light of wavelength lamda . The separation between the slits is d. The light transmitted by the slits falls on a screen Sigma_1 placed at a distance D from the slits. The slit S_3 is at the placed central line and the slit S_4 , is at a distance z from S_3 . Another screen Sigma_2 is placed a further distance D away from 1,1. Find the ratio of the maximum to minimum intensity observed on Sigma_2 if z is equal to a. z=(lamdaD)/(2d) b. (lamdaD)/d c. (lamdaD)/(4d)

Knowledge Check

  • Two identical narrow slits S_(1) and S_(2) are illuminated by light of wavelength lambda from a point source P. If, as shown in the diagtam above the light is then allowed to fall on a scree, and if n is a positive integer, the condition for destructive interference at Q is that

    A
    `(l_(1)-l_(2))= (2n+1)lambda//2`
    B
    `(l_(3)-l_(4))= (2n+1)lambda//2`
    C
    `(l_(3)+l_(3))-(l_(2)+l_(4))= n lambda`
    D
    `(l_(1)+l_(3))-(l_(2)+l_(4)) = (2n+1)lambda//2`

  • Two identical light sources S_1 and S_2 emit light of same wavelength lambda . These light rays will exhibit interference if

    A
    (a) Their phase differences remain constant
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    (b) Their phases are distributed randomly
    C
    (c) Their light intensities remain constant
    D
    (d) Their light intensities change randomly

  • Two slits, 4 mm apart, are illuminated by light of wavelength 6000 Å . What will be the fringe width on a screen placed 2 m from the slits

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    D
    `4.0 mm`

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