Section 6.5: Diffraction

Diffraction is the bending of waves around obstacles or through narrow openings. It is significant when the size of the obstacle or slit is comparable to the wavelength of light.

  • Single-slit diffraction: Light spreads out after passing through a narrow slit; central maximum is brightest and widest.
  • Double-slit interference (diffraction pattern): Combination of diffraction and interference produces bright and dark fringes on a screen.
  • The position of minima for a single slit of width \(a\): \[ a \sin \theta = m \lambda, \quad m = \pm 1, \pm 2, \dots \]
  • Fringe spacing for double slit: \[ \Delta y = \frac{\lambda L}{d} \] where \(L\) = screen distance, \(d\) = slit separation.

Example: Single-slit Diffraction

Light of wavelength 600 nm passes through a slit of width 0.2 mm. Find the angle for the first diffraction minimum.

Using \( a \sin \theta = m \lambda \) with \( m = 1 \): \( 0.2 \times 10^{-3} \sin \theta = 600 \times 10^{-9} \) \( \sin \theta = 3 \times 10^{-3} \) → \( \theta \approx 0.172° \)

Practice Problems

  1. Two slits are separated by 0.5 mm and light of wavelength 500 nm is used. Calculate the fringe spacing on a screen 2 m away.
  2. Determine the angle of the second minimum in a single-slit diffraction for a slit 0.1 mm wide and light of wavelength 600 nm.
  3. Explain why diffraction effects are more noticeable for longer wavelengths.
  4. A laser passes through a narrow slit and produces a central bright fringe of width 2 mm on a screen 1 m away. Find the slit width if the laser wavelength is 650 nm.
  5. Sketch the intensity pattern for single-slit diffraction.
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