Question

the real depth of the liquid is 4cm. the coin placed in the liquid appears to be raised by 1cm. find the refractive index of the liquid. hence name of the liquid

Answer 1

The medium is water and its refractive index is 1.333.

The relation between refractive index (n) of a medium, real depth (d1) and apparent depth (d2) is given by the formula:

n = d1 / d2

Substituting values, n = 4 / 3 = 1.333

Answer 2

Hello Dear.

Given ⇒
Real Depth = 4 cm.
Shift = 1 cm.
∴ Apparent Depth = 4 - 1
 = 3 cm.

Using the Formula,
   μ = Real Depth/Apparent Depth.
⇒ μ = 4/3
 ∴ μ = 1.33


Hence, the Refractive Index of the Liquid is 1.33.

Now, For Naming the Liquid, let us find the speed of the light in the liquid.

Refractive Index = Speed of the light in air/Speed of the Light in liquid.
4/3 = 3 × 10⁸/Speed of the light in liquid.
⇒ Speed of the light in the liquid = 2.25 × 10⁸ m/s.


We know, the the speed of the light in water is 2.25 × 10 m/s. Hence, the liquid is water.


Hope it helps.