Question

In Young's double-slit experiment, a slab of thickness $1.2\mu m$ and refractive index $1.5$ is placed in front of one slit and another slab of thickness $t$ and refractive index $2.5$ is placed in front of the second slit. If the position of the central fringe remains unaltered, then the thickness $t$ is-

• A. $0.4\mu m$
• B. $0.8\mu m$
• C. $1.2\mu m$
• D. $7\mu m$

Answer 1

Answer: (A)

$\because$ Central fringe at same position.
$\therefore$ Path difference $(\Delta x)=0$
Now $\left({\left(\mu \right)}_1-1\right)t_1=\left({\left(\mu \right)}_2-1\right)t_2$
$$\begin{gathered} (1.5-1)\times 1.2=(2.5-1)t \\ t=\frac{0.5\times 1.2}{1.5}=0.4\mu m \end{gathered}$$