Question

A tank is filled with water to a height of $12.5cm$. If the refractive index of water is $1.33$ then the apparent depth of a needle lying at the bottom of the tank as measured by a microscope is to be

Answer 1

Hint Tank height is given so real depth and refractive index is given so apparent depth can be measured by the direct formula of the refractive index.
Formula Used
We will use following formula to solve the problem:
Real depth/apparent depth = refractive index

Complete Step by step solution
As we know that the real Depth is actually the distance of an object beneath the surface, as it is measured by submerging a perfect ruler along with it.
And the apparent depth in a medium is the depth of an object in a denser medium as seen from the rarer medium.
So, its value is smaller than the real depth.
The Refractive Index is a value which is calculated from the ratio of the speed of light in a vacuum to that in a second medium of greater density.
Tank is filled with water to a height of$12.5cm$. Hence, this is the real depth of the object.
Refractive index of water is $1.33$
So now we need to find the apparent depth
So by using the formula directly we can get the value of the refractive index as:
Real depth/Apparent depth = Refractive Index
$\dfrac{12.5}{1.33}=\mu$
$=9.3cm$

Additional Information
The apparent depth of a tank of water changes when viewed obliquely. This happened due to the light bends on travelling medium from one medium to another.

Note
So real height is the real depth and we need to know the refractive index of that particular object. And the other one can easily be derived from the given values.