An experiment is performed to find the refractive index of glass using a travelling microscope. In t

Q: Why can't we just use a screw gauge for this?

A screw gauge is excellent for measuring the thickness of wires or thin sheets by gripping them between its jaws. However, a travelling microscope needs to measure the distance a lens travels to focus on an object, which requires a linear sliding scale, not a rotating screw mechanism.

Q: What exactly is a travelling microscope?

It is a compound microscope mounted on a vertical and horizontal track. It allows you to focus on an object and then measure exactly how far the microscope had to move to focus on a different object (like an image formed by refraction).

Q: Why is a standard meter scale not enough?

A standard meter scale has a least count of $1\text{ mm}$. When measuring apparent depth, the differences can be fractions of a millimeter. A $1\text{ mm}$ error would lead to a massive error in the calculated refractive index.

Q: How does the vernier scale on the microscope work?

It works exactly like the vernier scale on a Vernier Caliper. You read the main scale mark just before the vernier zero, and then find which vernier division perfectly aligns with a main scale division to get the fractional value.

Q: Is the least count always $0.01\text{ mm}$?

While $0.01\text{ mm}$ is the most common least count for laboratory travelling microscopes, it can vary depending on the specific design (e.g., how many vernier divisions correspond to main scale divisions).

Question

An experiment is performed to find the refractive index of glass using a travelling microscope. In this experiment, distances are measured by

Options:

(A) a vernier scale provided on the microscope

(B) a standard laboratory scale

(C) a meter scale provided on the microscope

(D) a screw gauge provided on the microscope

Sigma Percentile · Accepted Answer

### The Quest for Precision

Imagine you are in a physics laboratory, tasked with finding the refractive index of a thick glass slab. The fundamental principle relies on the optical illusion of depth. When you look through the glass, the bottom surface appears slightly raised. This is the apparent depth.

The formula for the refractive index is beautifully simple:

$$ \mu = \frac{	ext{Real Depth}}{	ext{Apparent Depth}} $$

However, the challenge lies not in the math, but in the measurement. How do you accurately measure the distance a microscope must travel to focus first on the bottom of the slab, and then on a mark viewed through the slab?

### The Limitations of Standard Scales

Your first instinct might be to use a standard laboratory scale or a meter rule. But let's think about the precision. A standard meter scale has a least count of $1	ext{ mm}$.

In optical experiments, the difference between real and apparent depth might be just a few millimeters. If your measuring instrument can only resolve down to $1	ext{ mm}$, your percentage error will be massive. A tiny misreading could completely ruin your calculation of the refractive index. We need something much more precise.

### Enter the Vernier Scale

To overcome this limitation, physicists use a **travelling microscope**. This is essentially a high-quality compound microscope mounted on a rigid vertical and horizontal track.

But the real magic lies in its measuring mechanism. Attached directly to the main scale of the microscope is a **Vernier scale**. By allowing a secondary sliding scale to interpolate between the marks of the main scale, the travelling microscope can achieve a least count of typically $0.01	ext{ mm}$.

This means you can measure the microscopic vertical travel of the lens with incredible accuracy, ensuring your refractive index calculation is spot on.

### The Final Verdict

Therefore, when performing an experiment to find the refractive index of glass using a travelling microscope, the distances are not measured by a simple meter scale or a screw gauge. They are measured by the highly precise **vernier scale provided on the microscope**.

Animated Solution for Physics - Optics: An experiment is performed to find the refractive index of glass using a travelling microscope. In this experiment, distances are measured by

Select Answer:

Visualized Solution

The Travelling Microscope

Need for Precision

The Vernier Scale

Conclusion

The Sigma Insight: Optical Instruments

The Quest for Precision

The Limitations of Standard Scales

Enter the Vernier Scale

The Final Verdict

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