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 solve the problem of finding the thickness of the glass slab with an air bubble, we will follow these steps:

### Step 1: Understand the Apparent Depth
When viewing the air bubble from one side of the glass slab, it appears to be at a certain depth due to refraction. The apparent depth (d_apparent) is given as:
- From one side (d1_apparent) = 6 cm
- From the opposite side (d2_apparent) = 4 cm

### Step 2: Use the Formula for Actual Depth
The relationship between the actual depth (d_actual) and the apparent depth can be expressed using the formula:
\[ d_{actual} = d_{apparent} \times \mu \]
where \( \mu \) is the refractive index of the medium (in this case, glass).

### Step 3: Calculate the Actual Depth from One Side
Using the formula for the first side:
\[ d_{1_{actual}} = d_{1_{apparent}} \times \mu \]
Substituting the values:
\[ d_{1_{actual}} = 6 \, \text{cm} \times 1.5 = 9 \, \text{cm} \]

### Step 4: Calculate the Actual Depth from the Opposite Side
Using the formula for the opposite side:
\[ d_{2_{actual}} = d_{2_{apparent}} \times \mu \]
Substituting the values:
\[ d_{2_{actual}} = 4 \, \text{cm} \times 1.5 = 6 \, \text{cm} \]

### Step 5: Calculate the Total Thickness of the Glass Slab
The total thickness (T) of the glass slab is the sum of the actual depths from both sides:
\[ T = d_{1_{actual}} + d_{2_{actual}} \]
Substituting the values:
\[ T = 9 \, \text{cm} + 6 \, \text{cm} = 15 \, \text{cm} \]

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

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