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 `(3"/"2)x`. The refractive index of second plate is

Explanation

To solve the problem, we need to understand the relationship between the refractive index of the glass plates and the fringe shift in a Young's double slit experiment. Here's the step-by-step solution:

### Step 1: Understand the fringe shift formula
In a Young's double slit experiment, the fringe shift (Δy) caused by introducing a plate of thickness \( t \) and refractive index \( \mu \) is given by the formula:
\[ \Delta y = \frac{t (\mu - 1) D}{d} \]
where:
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