A ray of light falls at an angle of `30^(@)` onto a plane-parallel glass plate and leaves it parallel to the initial ray. The refractive index of the glass is `1.5`. What is the thickness of `d` of the plane if the distances between the rays is `3.82cm` ? [Given: `sin^(-1) ((1)/(3)) = 19.5^(@), cos 19.5^(@) = 0.94, sin 10.5^(@) = 0.18`]

Explanation

To solve the problem step by step, we will follow these instructions:

### Step 1: Understand the Geometry of the Problem
We have a ray of light incident at an angle of \(30^\circ\) on a plane-parallel glass plate with a refractive index of \(1.5\). The ray exits the plate parallel to its original path. We need to find the thickness \(d\) of the glass plate given that the distance between the incident and the refracted rays is \(3.82 \, \text{cm}\).

**Hint:** Draw a diagram to visualize the incident ray, the refracted ray inside the glass, and the exiting ray.

### Step 2: Apply Snell's Law
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