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

The path difference introduced by a plate of thickness f and refractive index p is given by Δ=(μ−1)t A path difference of l, introduces a phase shift of β where β=λD/(2d) 2d = = separation between slits  So, a path difference of (μ−1)t introduces a shifts x on  he screen given by x=(μ−1)tβλ for first plate x= μ1−1tβλ for second plate 32x=μ2−1tβλ ∴ μ2−1μ1−1=32  or  μ2−1(1⋅5−1)=32 μ2=1.75