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 $\frac{3}{2}x=\frac{\left({\mu }_2-1\right)t\beta }{\lambda }$
$\Rightarrow \left(\frac{{\mu }_2-1}{{\mu }_1-1}\right)=\frac{3}{2}$
$\Rightarrow \left(\frac{{\mu }_2-1}{1.5-1}\right)=\frac{3}{2}$
$\Rightarrow {\mu }_2=1.75$