Question

In young's double slit experiment, the fringes are displaced by a distance 'y' 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 3y/2 . The refractive index of the second plate is?

Answer 1

In double slit experiment , displacement of fringes = $Y_0=\left(\mu -1\right)t\frac{D}{d}$
Where D = distance between slit and fringe, t = thickness of plate,

$$\begin{gathered} Y=\left(1.5-1\right)t\frac{D}{d}---\left(1\right) \\ Y\text{'}=\left(\mu -1\right)t\frac{D}{d}---\left(2\right) \end{gathered}$$
Given that Y'/Y= 3/2

Dividing equation (2) by (1)
$$\begin{gathered} \frac{Y\text{'}}{Y}=\frac{\left(\mu -1\right)t{\displaystyle \frac{D}{d}}}{\left(1.5-1\right)t{\displaystyle \frac{D}{d}}}=\frac{\mu -1}{\left(1.5-1\right)} \\ \frac{3}{2}=\frac{\mu -1}{0.5} \\ \mu -1=\frac{3}{4}\mu =\frac{3}{4}+1=\frac{7}{4}\mu =1.75 \end{gathered}$$