Question

In Young's double slit experiment, a mica slit of thickness $t$ and refractive index $\mu$ is introduced in the ray from the first source $S_1$. By how much distance the fringes pattern will be displaced?

• A. $\frac{d}{D}(\mu -1)t$
• B. $\frac{D}{d}(\mu -1)t$
• C. $\frac{d}{(\mu -1)D}$
• D. $\frac{D}{d}(\mu -1)$

Answer 1

The correct option is B $\frac{D}{d}(\mu -1)t$

Path difference generated due to insertion of mica sheet $\Delta x=(\mu -1)t$

Let the shift in the fringe pattern be $y$.

Also, path difference $\Delta x=\frac{yd}{D}$

So, $(\mu -1)t=\frac{yd}{D}$

$⟹y=\frac{(\mu -1)tD}{d}$

Option B is correct.