JEE Advance - Physics (2016 - Paper 2 Offline - No. 12)
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.
Which of the following is(are) true of the intensity pattern on the screen?
Which of the following is(are) true of the intensity pattern on the screen?
Semi circular bright and dark bands centered at point O
The region very close to the point O will be dark
Straight bright and dark bands parallel to the X-axis.
Hyperbolic bright and dark bands with foci symmetrically placed about O in the x-direction
Explanation
At point O, the path difference is
$${{2\pi } \over \lambda }({S_1}O - {S_2}O) = {{2\pi } \over \lambda }\left[ {\left( {D + {d \over 2}} \right) - \left( {D - {d \over 2}} \right)} \right]$$
$$ = {{2\pi d} \over \lambda } = {{2\pi (0.6003 \times {{10}^{ - 3}})} \over {600 \times {{10}^{ - 9}}}} = 2001\pi = (2n + 1)\pi $$
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.
Hence, option (B) is correct.
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