Question

Determine the refractive index of a glass slab using a travelling microscope.

Hint:

To ensure accuracy, always move the microscope in one direction (preferably upwards) when focusing to avoid backlash error in the screw mechanism. Use the fine adjustment knob for the final sharp focus and ensure that there is no parallax between the cross-wires of the eyepiece and the image being viewed.

Answer 1

Step 1: Understanding the Concept:
The refractive index (\(\mu\)) of a medium is defined as the ratio of the speed of light in vacuum to the speed of light in the medium. It can also be expressed as the ratio of the real depth to the apparent depth of an object viewed through the medium. A travelling microscope is a precision instrument used for measuring small distances, making it ideal for measuring the real and apparent depths of a glass slab.
Step 2: Key Formula and Apparatus:
Apparatus Required:
A travelling microscope, a rectangular glass slab, and a fine marker or lycopodium powder.
Key Formula:
Refractive Index \( \mu = \frac{\text{Real Depth}}{\text{Apparent Depth}} \)
In terms of microscope readings: \[ \mu = \frac{R_3 - R_1}{R_3 - R_2} \] where,
\(R_1\) = Microscope reading when focused on a mark without the slab.
\(R_2\) = Microscope reading when focused on the image of the mark seen through the slab.
\(R_3\) = Microscope reading when focused on the top surface of the slab.
Step 3: Detailed Procedure:
1. Reading R1: Place a mark (e.g., an ink cross) on a piece of paper on the base of the microscope. Adjust the microscope to focus sharply on this mark. Record the reading on the vertical vernier scale. This is \(R_1\).
2. Reading R2: Carefully place the glass slab over the ink mark without disturbing the setup. The mark will appear to be raised. Raise the microscope tube until the image of the mark is in sharp focus again. Record this new reading. This is \(R_2\).
3. Reading R3: Sprinkle a small amount of lycopodium powder or chalk dust on the top surface of the glass slab. Raise the microscope further to bring the powder particles into sharp focus. Record this reading. This is \(R_3\).
Step 4: Calculation:
1. Calculate the real depth of the glass slab: \( \text{Real Depth} = R_3 - R_1 \).
2. Calculate the apparent depth of the mark: This is given by the shift, which is \(R_1 - R_2\), but the depth itself in terms of readings is \(R_3 - R_2\).
3. Calculate the refractive index using the formula: \[ \mu = \frac{R_3 - R_1}{R_3 - R_2} \] Repeat the procedure two or three times to find the mean value of \(\mu\).