Question

A monochromatic beam of light falls on YDSE apparatus at some angle (say $\theta$) as shown in the figure. A thin sheet of glass is inserted in front of the lower slit $S_2$. The central bright fringe (path difference $=0$) will be obtained :

• A. at $O$
• B. above $O$
• C. below $O$
• D. anywhere depending on angle $\theta$, thickness of plate $t$, and refractive index of glass $\mu$

Answer 1

The correct option is D anywhere depending on angle $\theta$, thickness of plate $t$, and refractive index of glass $\mu$

The path difference between the incoming rays before they pass through the glass slab can be shown as $d\sin \theta$.

When light rays from both the slits interfere at $O$, the path diffrence due to the glass slab is $(\mu -1)t$, having the effect of path diffrence as opposite as that of the ray coming before the slits.

Hence if, $d\sin \theta =(\mu -1)t$, central fringe is obtained at $O$.

If $d\sin \theta >(\mu -1)t$, central fringe is obtained above $O$.

$d\sin \theta <(\mu -1)t$, central fringe is obtained below $O$.
$$\begin{array}{c}\text{Why this question?}\\ \text{Note : When rays are coming parallel from below the central axis at some}\\ \text{angle, the rays reaching the slit above the central axis has travelled more}\\ \text{path as compared to the rays reaching the slit below the central axis.}\end{array}$$