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 same thickness, the shift of fringes is $$\left( {\frac{3}{2}} \right)x.$$  The refractive index of second plate is

Solution :
Using relation, $${y_0} = \frac{D}{d}\left( {\mu - 1} \right)t$$
We have,
$$\eqalign{ & \frac{z}{{\frac{3}{2}z}} = \frac{{\left( {1.5 - 1} \right)}}{{\left( {\mu - 1} \right)}} \cr & \Rightarrow \frac{2}{3} = \frac{1}{{2\left( {\mu - 1} \right)}} \cr & \frac{1}{{\mu - 1}} = \frac{4}{3} \cr & \Rightarrow \mu - 1 = \frac{3}{4} \cr & \mu = \frac{7}{4} = 1.75 \cr} $$