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 $\left( S _{1}, S _{2}\right)$ 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 $d =0.6003\, mm$. 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 ?

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

Answer 1

Answer: (A), (B)

on the screen

At point near $O$
$\Delta x =0.6003\, mm$
$\Delta x =\frac{0.6003}{600 \times 10^{-6}} \lambda$
$\Rightarrow 1000.5 \lambda$
$\therefore $ near $O$ minima will occur