Question

In 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 (3/2) x. The refractive index of the second plate is

Answer 1

In Young's double slit experiment, when a glass slab is introduced in the path of one of the beam, fringes are displaced by a distance $x=\frac{D}{d}(\mu-1)t$

where , D is separation between slits and screen, d is separation between slits , t is thickness of slab.

now, from above, we can get the formula,

$\frac{x_1}{x_2}=\frac{\mu_1-1}{\mu_2-1}$

given, $x_1=x,x_2=\left(\frac{3}{2}\right)x$ and $\mu_1=1.5$

so, x/(3/2)x = (1.5 - 1)/($\mu_2$-1)

or, 1/1.5 = 0.5/($\mu_2$-1)

or, 0.75 = ($\mu_2$-1)

or, $\mu_2$ = 1.75

hence, refractive index of second plate is 1.75