Young Double Slit

Overview

Young double slit is one of the most important experiments in wave physics. It demonstrates the interference of Light Waves and provides strong evidence for its wave nature.

The experiment applies Superposition of Waves, Interference, wavelength, phase, and diffraction.

Definition

Young double slit is an experiment in which light from two closely spaced coherent slits overlaps on a screen, producing alternate bright and dark interference fringes.

Why It Matters

The experiment turns the abstract idea of phase into a visible pattern. It is central to light, optics, diffraction, and later wave-particle duality.

Key Representations

Basic Setup

A monochromatic light source first passes through a single slit and then through two closely spaced narrow slits.

• The single slit helps ensure a common wavefront reaches both slits.
• The two slits act as coherent sources.
• Light from the two slits overlaps on a distant screen.
• Alternate bright and dark fringes are observed.

Why a Single Source Is Needed

Two separate lamps are not normally coherent, even if they emit light of the same frequency.

The two slits must be illuminated by the same original source so that the waves emerging from them have:

• the same frequency;
• a constant Phase Difference.

Why Diffraction Is Also Needed

Each slit must be narrow enough for noticeable diffraction to occur. This allows light from the two slits to spread out and overlap.

Without sufficient diffraction, the two beams would not overlap enough to produce a visible interference pattern.

See Diffraction and Gratings.

Bright and Dark Fringes

Bright fringes are formed by constructive interference:

$$\Delta x=n\lambda$$

Dark fringes are formed by destructive interference:

$$\Delta x=\left(n+\frac{1}{2}\right)\lambda$$

At the centre of the screen, the path difference is zero:

$$\Delta x=0$$

so the central fringe is bright.

Geometry

Let:

• $a$ be slit separation;
• $D$ be distance from slits to screen;
• $x$ be fringe separation;
• $\lambda$ be wavelength.

For a point at angle $\theta$ to the centre line:

$$a\sin \theta =n\lambda$$

For small angles:

$$\sin \theta \approx \tan \theta \approx \frac{x}{D}$$

The position of the $n$th bright fringe is:

$$x_n=\frac{n\lambda D}{a}$$

The spacing between adjacent bright fringes is:

$$x=\frac{\lambda D}{a}$$

This formula assumes:

$$D\gg a$$

Meaning of the Fringe Spacing Formula

From:

$$x=\frac{\lambda D}{a}$$

• larger $\lambda$ gives larger fringe spacing;
• larger $D$ gives larger fringe spacing;
• larger $a$ gives smaller fringe spacing.

If the slits are moved further apart, the fringes get closer together.

Intensity

Intensity depends on amplitude squared:

$$I\propto A_0^2$$

If each slit contributes a wave of amplitude $A_0$, then at a bright fringe the resultant amplitude is $2A_0$:

$$I\propto (2A_0{)}^2=4A_0^2$$

At a dark fringe:

$$A_{\text{resultant}}=0$$

so:

$$I=0$$

If One Slit Is Covered

If one slit is blocked, interference disappears because only one wave reaches the screen.

At the original central bright fringe:

• original amplitude from two slits was $2A_0$;
• original intensity was proportional to $4A_0^2$.

With one slit covered:

• amplitude becomes $A_0$;
• intensity becomes proportional to $A_0^2$.

So the new central intensity is:

$$\frac{1}{4}$$

of the original central intensity.

White Light

White light contains many wavelengths. The central fringe is white, coloured fringes appear on both sides, and outer fringes blur because different wavelengths overlap differently.

Diffraction Envelope

In a real double-slit experiment, each slit has finite width. The actual pattern is an interference pattern modulated by a diffraction envelope. At this level, the main focus is usually the fringe spacing formula and the basic bright-dark pattern.

Formula Summary

Bright fringe:

$$\Delta x=n\lambda$$

Dark fringe:

$$\Delta x=\left(n+\frac{1}{2}\right)\lambda$$

Position of $n$th bright fringe:

$$x_n=\frac{n\lambda D}{a}$$

Fringe separation:

$$x=\frac{\lambda D}{a}$$

Links

• Core hub: Superposition of Waves
• Related: Interference
• Related: Diffraction and Gratings
• Related: Phase Difference
• Related: Light Waves
• Related: Superposition Common Exam Traps