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

# Order of Newton's ring with double diameter

Engineering Physics · Chapter 4: Physical Optics

- Asked in: 2073 Chaitra, 5 marks
- Video: [Solved Problems on Newton's Rings](https://www.youtube.com/watch?v=2aUUdOoq1ls) — Physics Jessy
- 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-double-diameter-order
- Whole chapter: https://www.bctengineer.com/md/semester_1/engineering_physics/chapter-4

## Question

Newton's rings are formed by sodium light viewed normally. What is the order of the dark ring which will have double the diameter of the 50th ring?

## Short answer

In Newton’s rings, D_n² ∝ n. D' = 2 D₅₀ gives D'²/D₅₀² = 4, so n' = 4 × 50 = 200. The 200th dark ring has double the diameter.

## Answer

For dark rings in reflected light (Newton's rings), D_n² = 4nλR, so the square of the diameter is proportional to the order *n*.

**Given:** D' = 2 D₅₀ (same λ and R).

1. D₅₀² = 4 × 50 × λR
2. D'² = (2D₅₀)² = 4 D₅₀² = 4 × (4 × 50 λR)
3. Also D'² = 4 n' λR, so n' = 4 × 50 = 200

```text
n' / 50 = (D' / D₅₀)² = 2² = 4   →   n' = 200
```

**Answer: the 200th dark ring has double the diameter of the 50th ring.**

## Check yourself

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

1. In Newton's rings (dark, reflected), D_n^2 is proportional to:
   A. n^2
   B. n
   C. sqrt(n)
   D. 1/n
   Answer: B. D_n^2 = 4nλR, so D^2 ∝ n for fixed λ and R. (Key point: D^2 proportional to n)

2. If the diameter doubles, D^2 becomes:
   A. 2 times
   B. 4 times
   C. 8 times
   D. Stays the same
   Answer: B. (2D)^2 = 4D^2. (Key point: Doubling the diameter)

3. Which ring has double the diameter of the 50th ring?
   A. 100th
   B. 150th
   C. 200th
   D. 2500th
   Answer: C. n'/50 = (D'/D)^2 = 4, so n' = 200. (Key point: Order)

## Related in Engineering Physics

- [Newton's rings with two wavelengths](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Anewton-rings-two-wavelengths-diameter) — Engineering Physics, chapter 4, asked 2×
- [Newton's rings vs Haidinger fringes](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Anewton-haidinger-bright-rings-transmitted) — Engineering Physics, chapter 4
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- [Number of bright Newton's rings](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Anewton-ring-bright-ring-count) — Engineering Physics, chapter 4
- [Coherent sources and Newton's ring law](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Anewton-rings-coherent-sources-diameter-law) — Engineering Physics, chapter 4

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