Question

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 ______.

Options

• `4/3`

• `3/2`

• `2/3`

• `6/5`

Answer 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 `bbunderline(3/2)`.

Explanation:

Let the real depth of the bubble from one face = x, cube side = 24 cm, refractive index = μ.

From the first side:

Apparent depth = `x/mu`

⇒ 12 = `x/mu`

⇒ x = 12 μ

From the opposite side:

`(24 - x)/mu = 4`

⇒ 24 − x = 4 μ

Substitute x = 12 μ:

24 − 12 μ = 4 μ

⇒ 24 = 16 μ

⇒ μ = `24/16`

= `3/2`