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. 8
B. 10
C. 12
D. 16

Explanation

To solve the problem of finding the thickness of the glass slab containing an air bubble, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We have a glass slab with a refractive index (n) of 1.5. An air bubble appears at different depths when viewed from two opposite surfaces of the slab: it appears 5 cm deep from one side and 3 cm deep from the other side.

2. **Define Variables**:
- Let \( d_1 \) be the actual depth of the bubble when viewed from the first surface (where it appears 3 cm deep).
- Let \( d_2 \) be the actual depth of the bubble when viewed from the second surface (where it appears 5 cm deep).
- The thickness of the slab is \( D \).

3. **Use the Apparent Depth Formula**: The apparent depth \( d' \) is related to the actual depth \( d \) and the refractive index \( n \) by the formula:
\[ d' = \frac{d}{n} \]
Rearranging gives:
\[ d = n \cdot d' \]

4. **Calculate Actual Depths**:
- From the first surface (where the bubble appears 3 cm deep):
\[ d_1 = n \cdot 3 = 1.5 \cdot 3 = 4.5 \text{ cm} \]
- From the second surface (where the bubble appears 5 cm deep):
\[ d_2 = n \cdot 5 = 1.5 \cdot 5 = 7.5 \text{ cm} \]

5. **Relate Thickness to Actual Depths**: The total thickness of the slab can be expressed as:
\[ D = d_1 + d_2 \]
Substituting the values we calculated:
\[ D = 4.5 \text{ cm} + 7.5 \text{ cm} = 12 \text{ cm} \]

6. **Conclusion**: The thickness of the glass slab is \( D = 12 \text{ cm} \).

### Final Answer:
The thickness of the slab is **12 cm**.