A bubble in glass slab `(mu = 1.5)` when viewed from one side appears at 5 cm and 2 cm from other side, then thickness of slab is :

Options

A. 3.75 cm
B. 3 cm
C. 10.5 cm
D. 2.5 cm

Answer

To solve the problem, we need to find the thickness of the glass slab based on the apparent distances of the bubble from both sides of the slab. Let's denote the following:

- \( \mu \) = refractive index of the glass slab = 1.5
- \( d_1 \) = apparent distance from one side = 5 cm
- \( d_2 \) = apparent distance from the other side = 2 cm
- \( x_1 \) = actual distance from the first side to the bubble
- \( x_2 \) = actual distance from the second side to the bubble
- \( t \) = thickness of the glass slab

### Step-by-Step Solution:

1. **Understanding Apparent Distance**:
The apparent distance can be related to the actual distance using the formula:
\[ d_{\text{apparent}} = \frac{d_{\text{actual}}}{\mu} \]

2. **Calculate Actual Distances**:
From the first side:
\[ d_1 = \frac{x_1}{\mu} \implies 5 = \frac{x_1}{1.5} \]
Rearranging gives:
\[ x_1 = 5 \times 1.5 = 7.5 \, \text{cm} \]

From the second side:
\[ d_2 = \frac{x_2}{\mu} \implies 2 = \frac{x_2}{1.5} \]
Rearranging gives:
\[ x_2 = 2 \times 1.5 = 3 \, \text{cm} \]

3. **Calculate Total Thickness**:
The total thickness of the slab \( t \) is the sum of the two actual distances:
\[ t = x_1 + x_2 = 7.5 + 3 = 10.5 \, \text{cm} \]

4. **Final Answer**:
Therefore, the thickness of the glass slab is:
\[ t = 10.5 \, \text{cm} \]