Question

A container of uniform cross-section has a height of 14 m. Upto what height should water of refractive index `4/3` be filled inside the container so that the container seems to be half filled for normal viewing?

Answer 1

Given:

Total height of container, H = 14 m

Refractive index of water, n = `4/3`​

Refractive index of air ≈ 1

Apparent depth of water = height of air column above water

Let the real height of the water filled be h.

Then height of air column above water = 14 − h

Formula:

Apparent depth of water = `"Real depth"/"Refractive index"`

`h/(4/3)` = 14 − h

`(3h)/4` = 14 − h

Multiply both sides by 4:

3h = 56 − 4h

7h = 56

h = `56/7`

h = 8 m