Question

While conducting 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 $600\text{nm}$. The student mistakenly placed the screen parallel to the $x-z$ plane $($for $z>0)$ at a distance $D=3\text{m}$, from the mid-point of $S_1,S_2$, as shown schematically in the figure. The distance between the sources $d=0.6003\text{mm}$. 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?

Answer 1

Fringes will be semicircular from YDSE theory.

The screen viewed from the front would look like

Here, every point in the semicircle will have the same path difference $\Delta x$.

Hence, semicircular bright and dark fringes will appear.
$\therefore$ options $\left(\text{C}\right)$ and $\left(\text{D}\right)$ are wrong.

Now to find the path difference at $O$ $\Delta x_o=d$

Let us assume that $n\lambda =d$

$n=\frac{d}{\lambda }=\frac{0.6003\text{mm}}{600\times {10}^{-9}\text{m}}=1000.5$

Hence, at $O$, $\Delta x=1000\lambda +\frac{\lambda }{2}$

Hence, it will be dark at $O$, which corresponds to minima. So we can say center point $O$ is minima and will be dark.

Therefore, the correct answer are $\left(\text{A}\right)$ and $\left(\text{B}\right)$.