---
title: "Third bright fringe separation, two wavelengths"
subject: "Engineering Physics"
chapter: 4
key: "semester_1/engineering_physics:double-slit-two-wavelengths-separation"
source: https://www.bctengineer.com/q/semester_1/engineering_physics/double-slit-two-wavelengths-separation
site: BCT Engineering
---

# Third bright fringe separation, two wavelengths

Engineering Physics · Chapter 4: Physical Optics

- Asked in: 2067 Asoj, 5 marks
- Video: [Worked examples: Overlapping fringes (two wavelengths) | Wave optics | Physics | Khan Academy](https://www.youtube.com/watch?v=xe1USWlX8qo) — Khan Academy India - English
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_1/engineering_physics/double-slit-two-wavelengths-separation
- Whole chapter: https://www.bctengineer.com/md/semester_1/engineering_physics/chapter-4

## Question

A light source emits light of two wavelengths 4300 Å and 5100 Å. The source is used in a double slit experiment. The distance between the sources and the screen is 1.5m and the distance between the slits is 0.025mm. Calculate the separation between the third order bright fringes due to the two wavelengths.

## Short answer

The position of the nth bright fringe is y_n = nλD/d. For n=3, Δy = 3D(λ₂−λ₁)/d = 3×1.5×(8×10⁻⁸)/(2.5×10⁻⁵) = 1.44×10⁻² m (14.4 mm).

## Answer

In Young's double-slit experiment the position of the *n*th bright fringe is y_n = nλD / d. Two wavelengths give fringes at different positions, and the separation of the third-order fringes is the difference of their positions.

**Given:** λ₁ = 4300 Å = 4.3 × 10⁻⁷ m, λ₂ = 5100 Å = 5.1 × 10⁻⁷ m, D = 1.5 m, d = 0.025 mm = 2.5 × 10⁻⁵ m, n = 3.

```text
y₁ = 3 × 4.3×10⁻⁷ × 1.5 / 2.5×10⁻⁵ = 7.74×10⁻² m = 77.4 mm
y₂ = 3 × 5.1×10⁻⁷ × 1.5 / 2.5×10⁻⁵ = 9.18×10⁻² m = 91.8 mm

Δy = y₂ − y₁ = 91.8 − 77.4 = 14.4 mm
```
Directly: Δy = nD(λ₂ − λ₁)/d = 3 × 1.5 × 8×10⁻⁸ / 2.5×10⁻⁵ = 1.44 × 10⁻² m.

**Answer: the third-order bright fringes are separated by 1.44 cm (14.4 mm).**

## Check yourself

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

1. What is the position of the nth bright fringe?
   A. nλD / d
   B. nD / (λd)
   C. (n+½)λD / d
   D. nλd / D
   Answer: A. y_n = nλD/d. (Key point: Fringe position)

2. How is the separation of the third-order fringes of the two wavelengths found?
   A. Add the two positions
   B. Subtract: Δy = nD(λ2 − λ1)/d
   C. Multiply the positions
   D. Use the average wavelength
   Answer: B. Both fringes lie on the same side; the separation is the difference of positions. (Key point: Method)

3. What is the separation (n = 3, D = 1.5 m, d = 0.025 mm, λ = 4300 Å and 5100 Å)?
   A. 1.44 mm
   B. 14.4 mm
   C. 144 mm
   D. 0.144 mm
   Answer: B. Δy = 3 × 1.5 × 8×10^-8 / 2.5×10^-5 = 1.44 × 10^-2 m = 14.4 mm. (Key point: Result)

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