Question

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

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

Answer 1

The correct option is D $1.75$

Shift =$\frac{(\mu -1)tD}{d}$

$x=\frac{(1.5-1)tD}{d}\dots \left(1\right)$

and
$\frac{3}{2}x=\frac{(\mu -1)tD}{d}\dots \left(2\right)$

Dividing equation $\left(1\right)$ by $\left(2\right)$

$\frac{2}{3}=\frac{0.5}{\mu -1}$

$2\mu -2=1.5$

$2\pi =3.5$

$\therefore \mu =1.75$

Hence, option $\left(\text{D}\right)$ is correct.