Question

In Young's double slit experiment, the fringes are displaced by a distance $x$ when a glass plate of one refractive index $1.5$ is introduced in the path of one of the beams. When this plate in replaced by another plate of the same thickness, the shift of fringes is $(3 / 2) x$. The refractive index of the second plate is

• A. 1.75
• B. 1.50
• C. 1.25
• D. 1.00

Answer 1

Answer: (A)

Fringe shift is given by $x=\frac{(\mu-1) t \beta}{\lambda}$. For first plate
$x=\frac{\left(\mu_{1}-1\right) t \beta}{\lambda}$
For second plate $\frac{3}{2} x=\frac{\left(\mu_{2}-1\right) t \beta}{\lambda}$
$\Rightarrow \left(\frac{\mu_{2}-1}{\mu_{1}-1}\right)=\frac{3}{2}$
$ \Rightarrow \left(\frac{\mu_{2}-1}{1.5-1}\right)=\frac{3}{2}$
$\Rightarrow \mu_{2}=1.75$