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

Answer

B, C

Explanation

Path difference at point O=d=.6003 mm
`=600300nm`
`=(2001)/(2)(600nm)=1000lamda+(lamda)/(2)`
`implies` minima form at point O
Line `S_(1)S_(2)` and screen are `bot` to each other so fringe pattern is circular (semi-circular because only half of screen is available).