Questions & explanations
1. Which of the following is NOT required in the refractive index of glass slab experiment using a travelling microscope?
- Metre scale
- Glass slab
- Lycopodium powder
- Spirit level
Answer: Spirit level
The experiment uses a travelling microscope to measure real and apparent depths; a spirit level is not needed because the microscope's vertical scale is calibrated and the slab is placed on a horizontal base. The principle is that refractive index = real depth / apparent depth, requiring only the slab, powder to mark surfaces, and a scale (metre scale or microscope scale) for depth measurement.
2. For a glass slab of real depth 2.00 cm, apparent depth 1.50 cm, and vernier least count 0.01 cm, what is the maximum possible error in n?
- 0.01
- 0.03
- 0.02
- 0.04
Answer: 0.02
Error in each reading is ±0.005 cm. Error in real depth = √(0.005²+0.005²) ≈ 0.007 cm. Error in apparent depth = same. Relative error in n = Δ(real)/real + Δ(apparent)/apparent = 0.007/2.00 + 0.007/1.50 = 0.0035 + 0.00467 ≈ 0.00817. So Δn = 0.00817 × 1.33 ≈ 0.0109 ≈ 0.01. But maximum possible error uses worst-case sum: Δn/n = (0.01/2.00)+(0.01/1.50)=0.005+0.00667=0.01167, so Δn=0.0155≈0.02.
3. In a travelling microscope experiment, the least count is 0.01 cm. Readings: R1 = 0.00 cm, R2 = 3.00 cm, R3 = 5.00 cm. What is the maximum percentage error in the refractive index n?
- 1.33%
- 0.67%
- 0.33%
- 0.89%
Answer: 1.33%
Refractive index n = (R3 - R1)/(R3 - R2) = 5.00/2.00 = 2.50. Each reading has error ±0.01 cm. Error in each difference = √(0.01²+0.01²) = 0.01414 cm. Relative error Δn/n = √[(0.01414/5.00)² + (0.01414/2.00)²] = 0.00707. Percentage error = 0.00707×100 = 0.707%. However, maximum error uses linear sum: Δn/n = 0.02/5.00 + 0.02/2.00 = 0.014, giving 1.4%. Closest option is 1.33%.
4. In the travelling microscope experiment to find refractive index of a glass slab, why is lycopodium powder sprinkled on the top surface instead of measuring slab thickness with a screw gauge?
- To reduce the apparent depth so that n becomes larger
- To make the slab surface visible since glass is transparent
- To avoid error from non-uniform thickness and ensure same vertical line is measured
- To prevent the slab from sliding during the experiment
Answer: To avoid error from non-uniform thickness and ensure same vertical line is measured
The lycopodium powder provides a diffuse reflecting surface on the same vertical line as the bottom mark, so the measured real depth (R3−R1) corresponds exactly to the same axial line as the apparent depth (R2−R1). Using a screw gauge externally would introduce independent errors and does not guarantee alignment, leading to inaccurate n.
5. In the travelling microscope experiment to find refractive index of a glass slab, after recording R1 (mark on paper), what is the next step?
- Sprinkle lycopodium powder on the slab and record R3.
- Place the glass slab over the mark and record R2 (image of mark).
- Remove the paper and place the slab directly on the base.
- Focus on the top surface of the slab and record R3.
Answer: Place the glass slab over the mark and record R2 (image of mark).
After recording R1 (mark on paper without slab), the next step is to place the glass slab over the mark, then refocus the microscope on the image of the mark (which appears higher due to refraction) and record this reading as R2. This follows the standard procedure in the NCERT Lab Manual.
6. Which of the following methods is used to measure the refractive index of a liquid using a travelling microscope?
- Apparent-depth method with a beaker
- Lens-mirror method with a convex lens
- Spectrometer method with a hollow prism
- Newton's rings method with a plano-convex lens
Answer: Apparent-depth method with a beaker
The travelling microscope apparent-depth method measures refractive index by comparing real and apparent depth. For a liquid, a beaker with a mark at the bottom is used; the microscope focuses on the mark directly and then through the liquid to find apparent depth.
7. A point object is at depth t in a medium of refractive index n. Light from it emerges into air. Using Snell's law and small-angle approximation, the apparent depth is:
- t (1 - 1/n)
- n t
- t / (n - 1)
- t / n
Answer: t / n
Using Snell's law: n sin i = sin r. For small angles, sin i ≈ tan i = x/t and sin r ≈ tan r = x/d', where x is lateral distance and d' is apparent depth. Substituting: n (x/t) = x/d' ⇒ d' = t/n. Thus apparent depth is real depth divided by refractive index.
8. In the travelling microscope experiment, if the glass slab has slightly non-parallel faces (wedge-shaped), the main effect on the measurement is:
- the apparent depth is measured correctly but the real depth is overestimated
- the image of the mark is laterally displaced, requiring horizontal adjustment of the microscope
- the least count of the microscope effectively increases
- the refractive index becomes exactly 1 due to total internal reflection
Answer: the image of the mark is laterally displaced, requiring horizontal adjustment of the microscope
A wedge-shaped slab acts like a thin prism, deviating the ray laterally. The image of the mark is displaced sideways, so the microscope must be moved horizontally to center the cross-wires. This introduces error in the vertical reading if not accounted for.
9. Why is a travelling microscope preferred over an ordinary metre scale for measuring apparent depth in the refractive index experiment?
- It has a larger least count, making readings easier.
- It has a smaller least count and eliminates parallax error.
- It can measure both depth and angle simultaneously.
- It is cheaper and more readily available.
Answer: It has a smaller least count and eliminates parallax error.
A travelling microscope has a least count of 0.01 cm, which is ten times better than an ordinary metre scale (0.1 cm). Additionally, the cross-wires in the eyepiece eliminate parallax error by ensuring the image and cross-wires are in the same plane.
10. A student reports the refractive index of a glass slab as 1.5000. The least count of the travelling microscope is 0.01 cm. Is this reporting correct?
- Yes, because n is a pure number.
- Yes, because the least count allows 4 decimal places.
- No, because n should have 5 significant figures.
- No, because n should have only 3 significant figures.
Answer: No, because n should have only 3 significant figures.
Each reading has 3 significant figures (e.g., 2.00 cm). The calculated n = real depth / apparent depth should be reported to the least number of significant figures among the measurements, which is 3. So n = 1.50 (3 s.f.), not 1.5000 (5 s.f.).
11. A travelling microscope is used in the refractive index experiment primarily to measure:
- vertical distances with high precision
- horizontal distances only
- both vertical and horizontal distances
- angular displacements
Answer: vertical distances with high precision
A travelling microscope is a compound microscope mounted on a vertical stand with a rack-and-pinion arrangement for precise vertical movement. It measures small vertical distances like real and apparent depth with a least count of 0.01 cm.
12. In the apparent-depth method for a liquid using a tall narrow beaker, which precaution is essential to avoid error due to meniscus?
- View the mark along the central axis of the beaker
- Use a wide beaker to reduce meniscus curvature
- Sprinkle lycopodium powder on the liquid surface
- Fill the beaker to a depth of at least 4–5 cm
Answer: View the mark along the central axis of the beaker
The meniscus at the walls causes the liquid surface to be curved; viewing off-centre would give an incorrect apparent depth. By viewing along the central axis, the line of sight is perpendicular to the surface, avoiding the curved region.