Question

Three immiscible transparent liquids with indices \(3/2\), \(4/3\) and \(6/5\) are arranged one above the other. The depths are \(3 \text{ cm}\), \(4 \text{ cm}\) and \(6 \text{ cm}\) respectively. The apparent depth of the vessel is.

• A. \(4 \text{ cm}\)
• B. \(6 \text{ cm}\)
• C. \(8 \text{ cm}\)
• D. \(10 \text{ cm}\)

Hint:

Apparent depth = Real depth Refractive index. Sum them up for multiple layers.

Answer 1

The Correct Option is D

Step 1: Formula
Total apparent depth \(d_{app} = \sum \frac{d_i}{\mu_i}\).

Step 2: Calculation
\(d_{app} = \frac{3}{3/2} + \frac{4}{4/3} + \frac{6}{6/5}\).
\(d_{app} = 2 + 3 + 5 = 10 \text{ cm}\).
Final Answer: (D)