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Young's Double Slit Experiment: The Complete Graphical Guide to Fringe Patterns

Visualize how fringe width changes with D, d, and λ. Master intensity variation graphs for JEE Physics.

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JEE Relevance
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Key Parameters
2min
Avg. Solve Time

Why Young's Experiment Matters in JEE

Young's Double Slit Experiment is the cornerstone of wave optics and appears in every JEE paper. Understanding the graphical relationships between parameters is crucial for solving problems quickly and accurately.

🎯 JEE Focus Areas

  • Fringe width calculation and variation
  • Intensity distribution graphs
  • Path difference and phase difference relationships
  • Effect of changing parameters (D, d, λ)
  • Position of maxima and minima

🚀 Quick Navigation

Basic Setup Fringe Width Intensity Graph Interactive Demo

1. Understanding the Basic Setup

The Experimental Arrangement

Young's experiment demonstrates the wave nature of light through interference patterns created by two coherent sources.

Key Components

  • Monochromatic source (S) - produces coherent light
  • Double slits (S₁ and S₂) - act as coherent sources
  • Screen - where interference pattern is observed
  • Distance D - between slits and screen
  • Slit separation d - distance between S₁ and S₂
Schematic Diagram
        Source S
           |
           |
        S₁ | S₂   (Double Slits)
         \ | /
          \|/
        ---+---  (Screen)
        Bright & Dark Fringes

Fundamental Formulas

Fringe Width (β):

$$ \beta = \frac{\lambda D}{d} $$

Where:
$\lambda$ = Wavelength of light
$D$ = Distance from slits to screen
$d$ = Distance between the two slits

Path Difference:

$$ \Delta x = \frac{yd}{D} $$

Where $y$ is the distance from central maximum

2. Fringe Width Variation with Parameters

How Fringe Width Changes

With Wavelength (λ)

$$ \beta \propto \lambda $$

Red light (λ ≈ 700 nm) gives wider fringes than blue light (λ ≈ 400 nm)

With Distance (D)

$$ \beta \propto D $$

Moving screen farther increases fringe width proportionally

With Slit Separation (d)

$$ \beta \propto \frac{1}{d} $$

Closer slits give wider fringes, farther slits give narrower fringes

Graphical Relationships

β vs λ (Keeping D, d constant)

Linear Relationship
λ (wavelength) →

β vs d (Keeping λ, D constant)

Inverse Relationship
d (slit separation) →

JEE Problem Example

Question: In Young's experiment, if the distance between slits is halved and screen distance is doubled, what happens to fringe width?

Solution:

Original: $\beta = \frac{\lambda D}{d}$

New: $d' = \frac{d}{2}$, $D' = 2D$

$\beta' = \frac{\lambda (2D)}{d/2} = \frac{4\lambda D}{d} = 4\beta$

Fringe width becomes 4 times larger

3. Intensity Variation Graph

Understanding the Interference Pattern

The intensity variation follows a cos² pattern due to the interference of two waves.

Intensity Formula:

$$ I = 4I_0 \cos^2\left(\frac{\phi}{2}\right) $$

Where:
$I_0$ = Intensity from single slit
$\phi$ = Phase difference between waves

Intensity Distribution

-3β -2β -β 0 β 2β 3β
Intensity
Position on Screen

🔍 Key Observations

  • Central maximum has maximum intensity ($4I_0$)
  • All bright fringes have same intensity ($4I_0$)
  • Dark fringes have zero intensity
  • Intensity decreases gradually in actual experiments due to slit width
  • The pattern is symmetrical about central maximum

Phase Difference Relationships

Condition Path Difference Phase Difference Intensity Fringe Type
$\Delta x = n\lambda$ $n\lambda$ $2n\pi$ $4I_0$ Bright
$\Delta x = (n+\frac{1}{2})\lambda$ $(n+\frac{1}{2})\lambda$ $(2n+1)\pi$ $0$ Dark

4. Interactive Fringe Pattern Demo

See How Parameters Affect Fringe Pattern

550 nm
2.0 mm
2.0 m
Fringe Width: 1.65 mm
Interactive Fringe Pattern Visualization

Adjust the sliders to see how each parameter affects the fringe pattern

📋 Quick Reference Guide

Key Formulas

  • Fringe width: $\beta = \frac{\lambda D}{d}$
  • Path difference: $\Delta x = \frac{yd}{D}$
  • Phase difference: $\phi = \frac{2\pi}{\lambda}\Delta x$
  • Intensity: $I = 4I_0 \cos^2\left(\frac{\phi}{2}\right)$
  • Position of nth maxima: $y_n = \frac{n\lambda D}{d}$

JEE Problem Solving Tips

  • Remember $\beta \propto \lambda$, $\beta \propto D$, $\beta \propto \frac{1}{d}$
  • Central fringe is always bright
  • All bright fringes have equal intensity
  • White light gives colored fringes with central white
  • For minima: $\Delta x = (n+\frac{1}{2})\lambda$

⚠️ Common JEE Mistakes to Avoid

❌
Confusing maxima and minima conditions

Maxima: $\Delta x = n\lambda$, Minima: $\Delta x = (n+\frac{1}{2})\lambda$

❌
Forgetting units conversion

λ in meters, D in meters, d in meters for consistent results

❌
Mixing up direct and inverse proportions

β ∝ λ and D, but β ∝ 1/d

❌
Ignoring the cos² nature of intensity

Intensity doesn't drop suddenly but follows cos² pattern

🎯 Practice Problems

1. In Young's experiment, the fringe width is 0.6 mm. If the entire apparatus is immersed in water (μ = 4/3), what will be the new fringe width?

Hint: Wavelength changes in medium

2. Two slits 0.2 mm apart are illuminated by light of wavelength 6000 Å. The interference fringes are observed on a screen 1 m away. Find the distance between 3rd bright fringe and 5th dark fringe.

Hint: Use positions formula

3. In a double slit experiment, the intensity at the central maximum is I₀. What will be the intensity at a point where the path difference is λ/4?

Hint: Use intensity formula with phase difference

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