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QJEEAdv16Ph0b97: JEE Advanced 2016 Physics - Class 12 JEEAdv16Ph0b97 Solution: While conducting the Young's double slit experiment, a student…

While conducting the Young's double slit experiment, a student replaced the two slits with a large opaque plate in the XY-plane containing two small holes that act as two coherent point sources (S1, S2) emitting light of wavelength 600 mm. The student mistakenly placed the screen parallel to the XZ-plane (for z > 0) at a distance D = 3 m from the mid-point of S1S2, as shown schematically in the figure. The distance between the source d = 0.6003 mm. The origin O is at the intersection of the screen and the line joining S1S2.

JEE Advanced 2016 Paper 2 Offline Physics - Wave Optics Question 13 English
Which of the following is(are) true of the intensity pattern on the screen?

Multiple Choice Options

  • A Semi circular bright and dark bands centered at point O
  • B The region very close to the point O will be dark
  • C Straight bright and dark bands parallel to the X-axis.
  • D Hyperbolic bright and dark bands with foci symmetrically placed about O in the x-direction

Step-by-Step Verified Solution

At point O, the path difference is

2πλ(S1O−S2O)=2πλ[(D+d2)−(D−d2)]{{2\pi } \over \lambda }({S_1}O - {S_2}O) = {{2\pi } \over \lambda }\left[ {\left( {D + {d \over 2}} \right) - \left( {D - {d \over 2}} \right)} \right]

=2πdλ=2π(0.6003×10−3)600×10−9=2001π=(2n+1)π= {{2\pi d} \over \lambda } = {{2\pi (0.6003 \times {{10}^{ - 3}})} \over {600 \times {{10}^{ - 9}}}} = 2001\pi = (2n + 1)\pi

Therefore, the dark fringe forms at O.

Hence, option (A) is correct.

The shape of wavefronts from both sources for D >> d is semi-circular, which are concentric with each other with the difference just in their phase resulting in concentric semicircular interference fringes. That is, the region nearby point O is dark.

JEE Advanced 2016 Paper 2 Offline Physics - Wave Optics Question 13 English Explanation

Hence, option (B) is correct.

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