Question

How much water should be filled in a container 21 cm in height, so that it appears half filled when viewed from the top of the container?

Answer 1

Hint: To solve this question we need to assume that the container should be filled with water and view from the top. Due to the phenomena of refractive index it appears half filled. Hence we can calculate the height of the water should be filled in the container by using the formula of refractive index.

Complete step by step solution:
From the given data:
Let the container be filled with water to a height of 'h' cm.
Then the part of the container which does not contain water is taken as (21-h) cm.
Therefore the apparent depth of the container filled with water should be (21-h) cm.
 We calculate the height by using the refractive index formula is given by
Refractive index = Real depth / apparent depth
$\mu = \dfrac{h}{{21 - h}}$
$\implies 1.33 = \dfrac{h}{{21 - h}}$
$\implies 1.33\left( {21 - h} \right) = h$
$\implies 27.93 - 1.33h = h$
$\therefore h = 12cm$
Hence, it results in 12cm of water being filled in a container.

Additional Information:
The apparent depth is the distance between the virtual image and from the surface of the water. The real depth is the distance between the real object and from the surface of the water.
The real depth is always larger than the apparent depth. As the real depth increases hence the apparent depth also increases.

Note:
When the ray of light travels from the denser medium to rarer medium then we need use the ratio of real depth to the apparent depth. Suppose When the ray of light travelling from the rarer medium to the denser medium then we need use the ratio of apparent depth to the real depth.