An air bubble inside a glass slab (µ=1.5) appears 6 cm when viewed from one side and 4 cm when viewed from the opposite side. The thickness of the slab is

Options

A. 10 cm
B. 6.67 cm
C. 15 cm
D. None of these

Explanation

To find the thickness of the glass slab containing an air bubble, we can use the apparent depth formula and the concept of refraction. Here’s a step-by-step solution:

### Step 1: Understand the Problem
We have an air bubble inside a glass slab with a refractive index (µ) of 1.5. The bubble appears to be 6 cm deep when viewed from one side and 4 cm deep when viewed from the opposite side.

### Step 2: Define Variables
Let:
- \( d_1 \) = apparent depth when viewed from one side = 6 cm
- \( d_2 \) = apparent depth when viewed from the opposite side = 4 cm
- \( t \) = thickness of the glass slab (what we need to find)
- \( d_{actual} \) = actual depth of the bubble

### Step 3: Use the Formula for Apparent Depth
The relationship between the actual depth and the apparent depth can be expressed as:
\[ d_{apparent} = \frac{d_{actual}}{\mu} \]
Where \( \mu \) is the refractive index of the medium (glass in this case).

### Step 4: Calculate Actual Depth from Each Side
1. From the first side:
\[ d_{actual1} = d_1 \times \mu = 6 \, \text{cm} \times 1.5 = 9 \, \text{cm} \]

2. From the second side:
\[ d_{actual2} = d_2 \times \mu = 4 \, \text{cm} \times 1.5 = 6 \, \text{cm} \]

### Step 5: Relate Actual Depths to Thickness
The total thickness of the slab can be found by adding the actual depths from both sides:
\[ t = d_{actual1} + d_{actual2} \]
Substituting the values we calculated:
\[ t = 9 \, \text{cm} + 6 \, \text{cm} = 15 \, \text{cm} \]

### Final Answer
The thickness of the glass slab is **15 cm**.

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