JEE Main 2023 · 12 April · morning · Single correct · +4 / −1

An ice cube has a bubble inside. When viewed from one side the apparent distance of the bubble is 12 cm. When viewed from the opposite side, the apparent distance of the bubble is observed as 4 cm. If the side of the ice cube is 24 cm, the refractive index of the ice cube is

  1. (a) 3/2
  2. (b) 4/3
  3. (c) 2/3
  4. (d) 6/5
Answer and solution

Answer (a) 3/2

Solution

Physics sir · 3 steps

The two real depths must add up to the cube's side, so add the two apparent depths together.

  1. Apparent depth rule. Seen through a flat face, an object at real depth x in a medium of index μ appears at depth x/μ.
  2. Both sides. Let the bubble be at real depth x from the first face. It is then at 24 - x from the opposite face. So x/μ = 12 and (24 - x)/μ = 4.

    x/μ + (24 - x)/μ = 24/μ = 12 + 4 = 16

  3. So. μ = 24/16 = 3/2, and the bubble is at x = 18 cm from the first face. The answer is (a).

The idea to keep. When an object is viewed from both sides of a slab, the apparent depths add up to thickness ÷ μ. You do not need the object's position to find μ.

Answer from the NTA final answer key. Solution by PrepWiser.

Study Ray Optics

Asked about 200 times in JEE Main since 2020. This question is from 2023.