Question

A beaker is filled with a liquid to a height of 14 cm. The apparent depth of a needle fixed at the bottom of the beaker is measured to be 10 cm by a microscope. What is the refractive index of the liquid? The height of the liquid in the beaker is now raised to 21 cm. By what distance would the microscope have to be moved to focus on the needle again?

Answer 1

Given:

Initial real depth of liquid, d₁ = 14 cm

Corresponding apparent depth, a₁ = 10 cm

New real depth, d₂ = 21 cm

To find: Refractive index, μ = ?

Calculation:

Step 1: Find the refractive index:

μ = `"Real depth"/"Apparent depth"`

= `14/10`

= 1.4​

Step 2: New apparent depth:

When the liquid height is increased to 21 cm.

New apparent depth = `21/μ`

= `21/1.4`

= 15 cm​

Step 3: Distance the microscope must move:

Initial apparent depth = 10 cm

New apparent depth = 15 cm

Therefore, the microscope needs to move by:

15 cm − 10 cm

= 5.0 cm