While conduction 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 600nm. The student mistakenly placed the screen parallel to the x-z plane `(for zgt0)` 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 `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 of the screen?

Options

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

Answer

B, D

Explanation

Path difference at `O=d=0.6003mm`
Now,=mm`300xx10^(-6) mm`
For `n=d` we get `n=2001`
As n is a whole number, the condition for minima is satisfied. Therefore `O` will be dark. Also, as the screen is perpendicular to the plane containing the slits, therefore fringes obtained will be semi-circular (Top half of the screen is available).