---
title: "Newton's ring diameter change with liquid"
subject: "Engineering Physics"
chapter: 4
key: "semester_1/engineering_physics:newton-ring-diameter-change-liquid"
source: https://www.bctengineer.com/q/semester_1/engineering_physics/newton-ring-diameter-change-liquid
site: BCT Engineering
---

# Newton's ring diameter change with liquid

Engineering Physics · Chapter 4: Physical Optics

- Asked in: 2072 Chaitra, 5 marks
- Video: [Interference Part 4: Diameters and applications of Newton's rings](https://www.youtube.com/watch?v=5mjXNUu5snM) — Dr. Sunita Dandwate
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_1/engineering_physics/newton-ring-diameter-change-liquid
- Whole chapter: https://www.bctengineer.com/md/semester_1/engineering_physics/chapter-4

## Question

In a Newton's ring experiment the diameter of the 10th ring changes from 1.40 cm to 1.27 cm when a liquid is introduced between the lens and the plate. Calculate the refractive index of the liquid.

## Short answer

Refractive index μ = (D_air/D_liquid)² = (1.40/1.27)² = 1.215 ≈ 1.22.

## Answer

In Newton's rings D_n² = 4nλR in air and D'_n² = 4nλR/μ with a liquid of index μ between lens and plate. Hence μ = D_n² / D'_n².

**Given:** D_10 (air) = 1.40 cm, D'_10 (liquid) = 1.27 cm.

1. Ratio of squares:

```text
μ = (1.40)² / (1.27)²
  = 1.9600 / 1.6129
  = 1.215
```

**Answer: refractive index of the liquid μ ≈ 1.22.**

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Which relation gives μ of the liquid in Newton's rings?
   A. μ = D_air / D_liquid
   B. μ = D_air^2 / D_liquid^2
   C. μ = D_liquid^2 / D_air^2
   D. μ = D_air^2 − D_liquid^2
   Answer: B. D_air^2 = 4nλR and D_liquid^2 = 4nλR/μ, so μ = D_air^2/D_liquid^2. (Key point: Formula with liquid)

2. Why does the ring diameter shrink in the liquid?
   A. The wavelength in the film is λ/μ, so rings form at smaller radii
   B. The lens becomes thicker
   C. R decreases
   D. The liquid absorbs light
   Answer: A. Optical thickness μt means the same order occurs at smaller thickness, hence smaller radius. (Key point: Ring size change)

3. For D = 1.40 cm (air) and 1.27 cm (liquid), μ is about:
   A. 1.10
   B. 1.22
   C. 1.48
   D. 0.82
   Answer: B. μ = 1.96/1.6129 = 1.215 ≈ 1.22. (Key point: Numerical result)

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