Expression for fringe width
Derivation and application of the formula for fringe width in Young's double-slit experiment.
What is Expression for fringe width?
The distance between the centers of two successive bright fringes or two successive dark fringes in an interference pattern.
Key formula / rule: Fringe Width
Key points
- Understand the concept of fringe width in interference patterns.
- Derive the formula for fringe width in Young's double-slit experiment.
- Analyze how changes in wavelength, slit separation, and screen distance affect fringe width.
- Apply the formula to solve problems related to interference patterns.
Common exam trap
Confusing the distance between slits (d) with the distance to the screen (D).
Definitions
- Term
Fringe Width (β)
- Meaning
The distance between the centers of two successive bright fringes or two successive dark fringes in an interference pattern.
- Term
Young's Double-Slit Experiment
- Meaning
An experiment demonstrating the wave nature of light by producing an interference pattern from two coherent sources (slits).
- Term
Interference
- Meaning
The phenomenon where two or more waves superpose to form a resultant wave of greater, lower, or the same amplitude.
Learning objectives
Understand the concept of fringe width in interference patterns.
Derive the formula for fringe width in Young's double-slit experiment.
Analyze how changes in wavelength, slit separation, and screen distance affect fringe width.
Apply the formula to solve problems related to interference patterns.
Formulae
- Name
Fringe Width
- Note
β: fringe width, λ: wavelength of light, D: distance of screen from slits, d: distance between slits.
- Expression
\β = \frac{\λ D}{d}
- Name
Position of nth Bright Fringe
- Note
n = 0, 1, 2, ...
- Expression
yn = \frac{n \λ D}{d}
- Name
Position of nth Dark Fringe
- Note
n = 0, 1, 2, ...
- Expression
yn = \frac{(2n+1) \λ D}{2d}
Prerequisites
Wave nature of light
Huygens' Principle
Diffraction
Interference (constructive and destructive)
Path difference
Phase difference
Common mistakes
Confusing the distance between slits (d) with the distance to the screen (D).
Incorrectly applying the path difference conditions for bright and dark fringes.
Forgetting to use consistent units for λ, D, and d.
Mistaking the distance between a bright and a dark fringe for the fringe width.
Keywords
Fringe width
Young's double-slit experiment
Interference
Wavelength
Slit separation
Screen distance
Constructive interference
Destructive interference
Path difference
Practice preview
In Young's double-slit experiment, if the distance between the slits is halved and the distance of the screen from the slits is doubled, then the fringe width will:…
easy
If monochromatic light of wavelength λ is replaced by light of wavelength λ/2 in Young's double-slit experiment, keeping other factors constant, the fringe width will:…
easy
In Young's double-slit experiment, fringes are formed on the screen. If the screen is moved away from the slits, the fringe width will:…
medium