Question 444: Wave Optics

Question

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 (S
1
, S
2
) 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 S
1
S
2
, 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 S
1
S
2
.
Which of the following is(are) true of the intensity pattern on the screen?
![](https://app-content.cdn.examgoal.net/fly/@width/image/1l0no0py2/c766b740-a7e4-4506-a9a7-0eb7ca19cc3e/94096ba0-a1e9-11ec-8b25-4fc5294790d5/file-1l0no0py3.png?format=png)

Accepted Answer

At point O, the path difference is
${{2\pi } \over \lambda }({S_1}O - {S_2}O) = {{2\pi } \over \lambda }\left[ {\left( {D + {d \over 2}} ight) - \left( {D - {d \over 2}} ight)} ight]$
$ = {{2\pi d} \over \lambda } = {{2\pi (0.6003 	imes {{10}^{ - 3}})} \over {600 	imes {{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.
![](https://app-content.cdn.examgoal.net/fly/@width/image/1l0rab3wv/20df9477-e2b8-4bb2-8aa3-8eac71cf9364/17b4f1f0-a3e7-11ec-9889-8ff85cf85963/file-1l0rab3ww.png?format=png)

Answer

Semi circular bright and dark bands centered at point O

Answer

The region very close to the point O will be dark

Answer

Straight bright and dark bands parallel to the X-axis.

Answer

Hyperbolic bright and dark bands with foci symmetrically placed about O in the x-direction

Wave Optics

Choose the correct answer: