Question

In a Young's double slit experiment, a sheet of thickness 100 µm and refractive index $1.5$ is introduced as shown in the figure. A sheet of thickness t and refractive index $2$ is introduced in lower ray's path. It is observed that there is no displacement in the fringes. The value of $t$ is

• A. $100\mu \text{m}$
• B. $200\mu \text{m}$
• C. $150\mu \text{m}$
• D. $50\mu \text{m}$

Answer 1

The correct option is D $50\mu \text{m}$

For no displacement in the fringes, the shift due to both slabs should cancel each other.
$({\mu }_1-1)t_1=({\mu }_2-1)t_2$
$(1.5-1)\times 100=(2-1)t_2$
$t_2=50\mu \text{m}.$