Question

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 $3\,cm$ deep when viewed from the opposite face. The thickness (in cm) of the slab is

• A. 8
• B. 10
• C. 12
• D. 16

Answer 1

The Correct Option is C

To solve this problem, let's consider the working principle of optics where the apparent depth and actual depth relationship is observed through a medium with a specific refractive index.

The formula for apparent depth \(d'\) when looking perpendicularly through a medium with refractive index \(n\) is given by:

d' = \frac{d}{n}

Where:

• d' is the apparent depth
• d is the actual depth
• n is the refractive index.

In the given problem:

• Refractive index, \(n = 1.5\)
• Apparent depth from one side, \(d_1' = 5 \, \text{cm}\)
• Apparent depth from the opposite side, \(d_2' = 3 \, \text{cm}\)

When viewing from both sides of the slab, each side will give a different apparent depth. For each view, the actual depth from that side will sum up to the thickness of the slab 't'. Let's calculate:

Step 1: Calculate actual depths

For the first side:

d_1 = n \times d_1' = 1.5 \times 5\, \text{cm} = 7.5\, \text{cm}

For the opposite side:

d_2 = n \times d_2' = 1.5 \times 3\, \text{cm} = 4.5\, \text{cm}

Step 2: Calculate the thickness of the slab

The actual depths sum up to the actual thickness of the slab. Thus:

d_1 + d_2 = t

7.5\, \text{cm} + 4.5\, \text{cm} = 12\, \text{cm}

Thus, the thickness of the slab is 12 cm.

Conclusion:

Therefore, the correct answer is 12.