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

1.75

$x=\frac{(μ-1)tβ}{λ}$

For first plate, $x=\frac{(μ_1-1)tβ}{λ}$

For second plate $\frac{3}{2}x=\frac{(μ_2-1)tβ}{λ}$

$∴\frac{(μ_2-1)}{(μ_1-1)}=\frac{3}{2}$

or $\frac{(μ_2-1)}{1.5-1)}=\frac{3}{2}$

$⇒μ_2=1.75$