Question

A microscope is focused on a mark on a piece of paper and then a slab of glass of thickness 3 cm and refractive index 1.5 is placed over the mark. How should the microscope be moved to get the mark in focus again?

• A. 1 cm upward
• B. 0.5 cm downward
• C. 1 cm downward
• D. 0.5 cm upward

Answer 1

The Correct Option is A

 To determine how much the microscope should be moved to focus on the mark again after placing a slab of glass over it, we need to understand how light behaves when it passes through the glass.

When a slab of glass with refractive index \(n\) and thickness \(t\) is placed over an object, the apparent shift in the position of the object is given by:

\(d = t \left(1 - \frac{1}{n}\right)\)

Where:

• \(d\) is the apparent shift in the position.
• \(t = 3 \, \text{cm}\) is the thickness of the glass slab.
• \(n = 1.5\) is the refractive index of the glass.

 

Substituting the given values into the formula:

\(d = 3 \left(1 - \frac{1}{1.5}\right) = 3 \times \left(1 - \frac{2}{3}\right) = 3 \times \frac{1}{3} = 1 \, \text{cm}\)

This means the mark appears to be shifted upwards by 1 cm due to the glass slab.

Thus, the microscope should be moved 1 cm upward to focus on the mark again.

The correct answer is: 1 cm upward