---
title: "Newton's rings: why circular, transmitted"
subject: "Engineering Physics"
chapter: 4
key: "semester_1/engineering_physics:newton-rings-circular-transmitted-theory"
source: https://www.bctengineer.com/q/semester_1/engineering_physics/newton-rings-circular-transmitted-theory
site: BCT Engineering
---

# Newton's rings: why circular, transmitted

Engineering Physics · Chapter 4: Physical Optics

- Asked in: 2068 Shrawan, 5 marks
- Video: [Why Are Newton's rings Circular ?](https://www.youtube.com/watch?v=XNw_AAlcOQY) — MathsInDepth (Decoding Science)
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_1/engineering_physics/newton-rings-circular-transmitted-theory
- Whole chapter: https://www.bctengineer.com/md/semester_1/engineering_physics/chapter-4

## Question

Why are Newton's rings circular? Discuss and derive the necessary theory of Newton's ring experiment for transmitted light.

## Short answer

Rings are circular because the air film thickness depends only on radial distance from the point of contact. In transmitted light, two internal reflections cancel phase changes, so the centre is bright. Bright rings: 2t = nλ, r_n = √(nλR); dark rings: 2t = (2n−1)λ/2, r_n² = (2n−1)λR/2.

## Answer

#### Why the rings are circular
A plano-convex lens of large radius of curvature *R* rests on a flat glass plate. The air film between them has a thickness *t* that depends only on the distance *r* from the point of contact, because the lens surface is a sphere (symmetric about the axis through the contact point). All points at the same *r* have the same thickness, so the loci of constant path difference are circles centred on the contact point.

#### Theory for transmitted light
```text
        light
          |
     _____|_____        lens (radius of curvature R)
    /     |     \
   ---------------      <- air film of thickness t
   ===============      glass plate
        P  O  P'
```
The ray transmitted straight through the film and the ray that is reflected twice inside the film (once at the plate, once at the lens surface) interfere. Both of these reflections take place at an air-to-glass boundary (first on the plate, then on the lens surface), and each gives a phase change of π. The two changes cancel, so there is no net phase change.

1. Path difference at normal incidence = 2μt (μ = 1 for air, so 2t).
2. Geometry: from the right triangle formed by the lens centre C, the foot of the perpendicular and the point on the lens surface, R² = (R − t)² + r² gives r² = 2Rt − t². Since t ≪ R, t² is neglected: **t = r² / 2R**.
3. Bright ring (maximum): 2t = nλ, so r²/R = nλ.
 **r_n = √(nλR)**, D_n² = 4nλR (n = 0, 1, 2, ...; n = 0 is the bright centre).
4. Dark ring (minimum): 2t = (2n − 1)λ/2.
 **r_n² = (2n − 1)λR / 2**, D_n² = 2(2n − 1)λR (n = 1, 2, ...).

#### Conclusions
- The centre of the transmitted pattern is **bright**; it is the complement of the reflected pattern (dark centre).
- Diameter of a bright ring is proportional to √n, so D_n² ∝ n and the rings get closer as n increases.
- Contrast is low in transmitted light because the two interfering beams have very different intensities.
- Wavelength can be found from D²_(n+p) − D²_n = 4pλR.

## Check yourself

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

1. Newton's rings are circular because:
   A. Film thickness depends only on distance from the contact point, due to the spherical lens surface
   B. The source is circular
   C. The plate is circular
   D. Light is polarized
   Answer: A. Points at equal r have equal thickness, so constant path difference loci are circles. (Key point: Why circular)

2. In transmitted light the net phase change is:
   A. π
   B. zero, since the two reflections each give π and cancel
   C. π/2
   D. 2π
   Answer: B. Both internal reflections are air-to-glass with π each, so they cancel. (Key point: Transmitted phase)

3. A bright ring in transmitted light occurs when:
   A. 2t = (2n−1)λ/2
   B. 2t = nλ, giving D_n^2 = 4nλR
   C. t = nλ
   D. 2t = nλ/2
   Answer: B. Path difference 2t = nλ with t = r^2/2R gives r^2 = nλR. (Key point: Bright ring)

4. The centre of the transmitted pattern is:
   A. dark
   B. bright, complementary to the reflected pattern
   C. coloured
   D. absent
   Answer: B. n = 0 gives a bright centre. (Key point: Centre)

## Related in Engineering Physics

- [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
- [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
- [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×
- [Order of Newton's ring with double diameter](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Anewton-ring-double-diameter-order) — Engineering Physics, chapter 4
- [Newton's rings, refractive index of liquid](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Anewton-rings-liquid-refractive-index) — Engineering Physics, chapter 4, asked 2×
- [Newton's rings between two curved surfaces](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Anewton-rings-two-curved-surfaces) — Engineering Physics, chapter 4

## Related in other subjects

- [Derive Newton-Raphson formula](https://www.bctengineer.com/question.md?key=semester_4%2Fnumerical_method%3Anewton-raphson-derive) — Numerical Method, chapter 2, asked 2×
- [Derive derivatives from Newton forward](https://www.bctengineer.com/question.md?key=semester_4%2Fnumerical_method%3Aderive-derivatives-newton-forward) — Numerical Method, chapter 5
- [Circular well 4 m, light and heavy well](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Acircular-well-4m-light-heavy) — Foundation Engineering, chapter 9
- [Circular ring with radial air gap, DC current](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Aring-outer-inner-diameter-radial-gap) — Electrical Machines, chapter 1