While conducting the Young's double slit experiment, a student replaced the two slits with a large opaque plate in the plane containing two small holes that act as two coherent point sources emitting light of wavelength 600 nm. [2016]

Question

While conducting the Young's double slit experiment, a student replaced the two slits with a large opaque plate in the $x - y$ plane containing two small holes that act as two coherent point sources $(S_{1}, S_{2})$ emitting light of wavelength 600 nm. The student mistakenly placed the screen parallel to the $x - z$ 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 sources is $d = 0.6003 mm$ . The origin O is at the intersection of screen and the line joining $S_{1} S_{2}$ . Which of the following is(are) true of the intensity pattern on the screen [2016]

Smart Achievers · Accepted Answer

(2, 4)

Path difference at $O$ $(S_{1}, S_{2})$

For $x - z$

we get $n = 2001$

As $n$ is a whole number, the condition for minima is satisfied.

Therefore, $' O'$ will be dark, i.e., minima is formed at $S_{1} S_{2}$ .

Also, as the screen is perpendicular to the plane containing the slits $S_{1}$ and $S_{2}$ , the fringes obtained will be semi-circular (only the top half of the screen is available)

Solution

1 Straight bright and dark bands parallel to the x-axis

2 The region very close to the point O will be dark

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

4 Semicircular bright and dark bands centered at point O

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