A tank filled with a liquid to a height of 12.5 cm. The apparent depth of a needle lying at the bottom of the tank is measured by a microscope to be 10 cm. If water is replaced by water of refractive index 1.66 up to the same height, by what distance (in mm) would the microscope have to be moved to focus on the needle again?

Explanation

To solve the problem, we will follow these steps:

### Step 1: Understand the given information
We have a tank filled with liquid (initially water) to a height of 12.5 cm. The apparent depth of a needle at the bottom of the tank is measured to be 10 cm. When the water is replaced by another liquid with a refractive index of 1.66, we need to find out how much the microscope must be moved to focus on the needle again.

### Step 2: Calculate the apparent depth with the new liquid
The formula for apparent depth (d') when the refractive index (μ) is known is given by:
\[ d' = \frac{h}{\mu} \]
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