Question

A tank is filled with a liquid to a height of 12.5 m. The apparent depth of a needle lying at the bottom of the tank is measured to be 9.0 m. Calculate the speed of light in the liquid.

Answer 1

Given: Real depth = 12.5 m

Apparent depth = 9.0 m

Speed of light in vacuum (c) = 3 × 10⁸ m/s

Refractive index of a medium (n) = `"Real depth"/"Apparent depth"`

n = `c/v`

= `12.5/9.0`

= 1.39

v = `c/n`

= `(3 xx 10^8)/1.39`

≈ 2.16 × 10⁸ m/s

∴ The speed of light in the liquid is 2.16 × 10⁸ m/s.