Question

A glass cube of length 24 cm has a small air bubble trapped inside. When viewed normally from one face it is 10 cm below the surface. When viewed normally from the opposite face, its apparent distance is 6 cm. The refractive index of glass is

• A. 1.50
• B. 1.40
• C. 1.45
• D. 1.55

Hint:

In normal viewing, apparent depth = real depth / refractive index. For a slab, the sum of apparent depths from opposite faces equals the actual thickness divided by \(\mu\) only if the bubble is at the centre? Here we solve directly.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
A glass cube of side 24 cm contains an air bubble. When viewed normally from one face, the apparent depth is 10 cm; from the opposite face, the apparent depth is 6 cm. We need the refractive index \(\mu\) of glass.

Step 2: Key Formula or Approach:
For normal viewing, apparent depth = real depth / \(\mu\).
Let the real distance of the bubble from the first face be \(x\). Then from the opposite face, the real distance is \(24 - x\).

Step 3: Detailed Explanation:
From first face: \(\frac{x}{\mu} = 10\) ⇒ \(x = 10\mu\).
From opposite face: \(\frac{24 - x}{\mu} = 6\) ⇒ \(24 - x = 6\mu\).
Substitute \(x = 10\mu\): \(24 - 10\mu = 6\mu\) ⇒ \(24 = 16\mu\) ⇒ \(\mu = 1.5\).

Step 4: Final Answer:
The refractive index is 1.50, option (A).