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 depths of a bubble viewed from two sides. Let's break down the solution step by step.

### Step-by-Step Solution:

1. **Understanding Apparent Depths**:
- When viewed from one side, the bubble appears at a depth of 5 cm (let's call this \( y_1 \)).
- When viewed from the other side, it appears at a depth of 2 cm (let's call this \( y_2 \)).

2. **Total Apparent Depth Calculation**:
- The total apparent depth \( y \) is the sum of the two apparent depths:
\[ y = y_1 + y_2 = 5 \, \text{cm} + 2 \, \text{cm} = 7 \, \text{cm} \]

3. **Using the Formula for Apparent Depth**:
- The relationship between the real depth \( x \) (which is the thickness of the slab) and the apparent depth \( y \) is given by:
\[ y = \frac{x}{\mu} \]
- Here, \( \mu \) (the refractive index of the glass) is given as 1.5.

4. **Rearranging the Formula**:
- To find the real depth \( x \), we rearrange the formula:
\[ x = \mu \cdot y \]

5. **Substituting the Values**:
- Now, substituting the values we have:
\[ x = 1.5 \cdot 7 \, \text{cm} \]
- Calculating this gives:
\[ x = 10.5 \, \text{cm} \]

6. **Conclusion**:
- Therefore, the thickness of the glass slab is:
\[ \text{Thickness of the slab} = 10.5 \, \text{cm} \]