Wave Behavior of Light: Understanding Diffraction and Young's Double Slit Experiment

Expert reviewed • 22 November 2024 • 6 minute read

Introduction

When light encounters obstacles or openings comparable to its wavelength, it exhibits a fascinating behavior known as diffraction. This phenomenon, along with Young's famous double-slit experiment, provides compelling evidence for the wave nature of light.

The Nature of Diffraction

Diffraction occurs when a wave encounters an obstacle or passes through an opening. The wave spreads out and bends around obstacles or through apertures, with the degree of spreading dependent on two key factors:

  • The wavelength of the light
  • The size of the opening or obstacle

When light passes through a narrow slit:

  • If the slit width is comparable to or smaller than the wavelength, significant diffraction occurs
  • Larger slit widths result in less noticeable diffraction
  • The smaller the slit, the greater the diffraction effect

Huygens' Principle

In the 17th century, Christiaan Huygens proposed a model that explains diffraction through the concept of wavelets:

According to Huygens' principle:

  • Every point on a wavefront acts as a source of secondary spherical wavelets
  • These wavelets combine to form the new wavefront
  • When part of the wavefront is blocked, the resulting wave pattern shows diffraction

Young's Double-Slit Experiment

In 1801, Thomas Young performed his groundbreaking double-slit experiment, which demonstrated light's wave nature:

The experimental setup consists of:

  • A monochromatic light source
  • Two narrow, parallel slits
  • A viewing screen

The resulting pattern shows:

  • Alternating bright and dark bands (interference pattern)
  • A central maximum of greatest intensity
  • Symmetrical maxima of decreasing intensity on either side

Mathematical Analysis

The positions of bright and dark bands can be predicted using interference equations:

For constructive interference (bright bands): dsin⁡(θ)=mλd\sin(\theta) = m\lambda

For destructive interference (dark bands): dsin⁡(θ)=(m+12)λd\sin(\theta) = (m + \frac{1}{2})\lambda

Where:

  • dd = slit separation
  • θ\theta = angle from the central maximum
  • mm = order number (0, ±1, ±2,...)
  • λ\lambda = wavelength of light

The maximum number of visible orders (mmaxm_{max}) is given by: mmax=⌊dλ⌋m_{max} = \left\lfloor\frac{d}{\lambda}\right\rfloor

Diffraction Gratings

Multiple parallel slits (diffraction gratings) produce sharper interference patterns:

  • More slits create higher intensity maxima
  • Dark regions become more defined
  • The basic equation dsin⁡(θ)=mλd\sin(\theta) = m\lambda still applies

White Light Diffraction

When white light undergoes diffraction:

  • Each wavelength diffracts at a different angle
  • This creates rainbow-like spectra
  • Red light (longer wavelength) diffracts more than blue light
  • Multiple orders of spectra may be visible, decreasing in intensity

Applications

Understanding diffraction has led to numerous applications:

  • Spectroscopy for chemical analysis
  • Optical instruments resolution limits
  • X-ray crystallography
  • Fiber optic communications

Up Next

Historical Models of Light: Newton vs Huygens

Return to Module 7: The Nature of Light