An air bubble in a glass slab with refractive index `1.5` (near normal incidence) is `5 cm` deep when viewed from one surface and `3cm` deep when viewed from the opposite face. The thickness (in `cm)` of the slab is

Options

A. 12
B. 16
C. 8
D. 10

Explanation

To solve the problem, we need to find the thickness of the glass slab given the apparent depths of an air bubble when viewed from both sides. Here’s a step-by-step solution:

### Step 1: Understand the Problem
We have a glass slab with a refractive index (μ) of 1.5. An air bubble inside the slab appears to be at a depth of 5 cm when viewed from one side and 3 cm when viewed from the opposite side. We need to find the actual thickness of the slab.

### Step 2: Use the Formula for Apparent Depth
The formula for apparent depth is given by:
\[ \text{Apparent Depth} = \frac{\text{Actual Depth}}{\mu} \]
From this, we can express the actual depth (D1 and D2) in terms of the apparent depth.

### Step 3: Set Up the Equations
1. When viewed from the first side (where the apparent depth is 5 cm):
\[ D1 = \mu \times \text{Apparent Depth}_1 = 1.5 \times 5 \text{ cm} \]
\[ D1 = 7.5 \text{ cm} \]

2. When viewed from the other side (where the apparent depth is 3 cm):
\[ D2 = \mu \times \text{Apparent Depth}_2 = 1.5 \times 3 \text{ cm} \]
\[ D2 = 4.5 \text{ cm} \]

### Step 4: Calculate the Total Thickness of the Slab
The total thickness of the slab (D) is the sum of the actual depths from both sides:
\[ D = D1 + D2 = 7.5 \text{ cm} + 4.5 \text{ cm} \]
\[ D = 12 \text{ cm} \]

### Conclusion
The thickness of the glass slab is **12 cm**.

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