---
title: "Double slit fringe separation numerical"
subject: "Engineering Physics"
chapter: 4
key: "semester_1/engineering_physics:young-double-slit-fringe-separation"
source: https://www.bctengineer.com/q/semester_1/engineering_physics/young-double-slit-fringe-separation
site: BCT Engineering
---

# Double slit fringe separation numerical

Engineering Physics · Chapter 4: Physical Optics

- Asked in: 2068 Shrawan, 5 marks
- Video: [Fringe width in Young's double slit experiment | Wave optics | Physics | Khan Academy](https://www.youtube.com/watch?v=HngUjqjsFAg) — 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/young-double-slit-fringe-separation
- Whole chapter: https://www.bctengineer.com/md/semester_1/engineering_physics/chapter-4

## Question

A screen containing two slits 0.1mm apart is 1m from the viewing screen. Light of wavelength λ = 500 nm falls on the slits from a distant source. Approximately how far apart will the bright interference fringes be seen on the screen?

## Short answer

Using β = λD/d with λ=500 nm, D=1 m, d=0.1 mm gives β = 5×10⁻³ m. Adjacent bright fringes are approximately 5 mm apart.

## Answer

In Young's double-slit experiment, the bright fringes are equally spaced. The fringe separation (fringe width) is β = λD / d, valid for small angles.

**Given:** d = 0.1 mm = 1 × 10⁻⁴ m, D = 1 m, λ = 500 nm = 5 × 10⁻⁷ m.

```text
β = λD / d
  = (5×10⁻⁷ × 1) / (1×10⁻⁴)
  = 5×10⁻³ m
```
**Answer: adjacent bright fringes are about 5 mm apart.**

**Check:** path difference for the first bright fringe is d sin θ = λ, so θ ≈ λ/d = 5 × 10⁻³ rad, and y = Dθ = 5 mm, which agrees.

## Check yourself

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

1. Which formula gives the separation of adjacent bright fringes in Young's experiment?
   A. β = λd / D
   B. β = λD / d
   C. β = dD / λ
   D. β = λ / (dD)
   Answer: B. Fringe width is β = λD/d for small angles. (Key point: Fringe width formula)

2. What value of d must be substituted for slits 0.1 mm apart?
   A. 1 × 10^-7 m
   B. 1 × 10^-3 m
   C. 1 × 10^-4 m
   D. 0.1 m
   Answer: C. 0.1 mm = 1 × 10^-4 m; using consistent SI units is essential. (Key point: Unit conversion)

3. What is the fringe separation for λ = 500 nm, D = 1 m, d = 0.1 mm?
   A. 0.5 mm
   B. 5 mm
   C. 50 mm
   D. 5 µm
   Answer: B. β = 5×10^-7 × 1 / 1×10^-4 = 5×10^-3 m = 5 mm. (Key point: Result)

## Related in Engineering Physics

- [Third bright fringe separation, two wavelengths](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Adouble-slit-two-wavelengths-separation) — Engineering Physics, chapter 4
- [Fringe width of air wedge numerical](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Awedge-fringe-width-wire-numerical) — Engineering Physics, chapter 4
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