Wave Optics and Diffraction

Wave Optics

• Deals with light interacting with objects comparable to its wavelength.
• Light has wavelengths less than a micron.

Electromagnetic Waves

• Light obeys the equation: $v = f \lambda$
• In a vacuum: $c = f \lambda$, where $c = 3 \times 10^8 m/s$
• Refractive index changes wavelength: $\lambda = \frac{\lambda_n}{n}$

Diffraction

• Bending of a wave around edges of an opening or obstacle.
• More narrow opening = more diffraction.

Ray vs Wave Optics

• Ray Optics: \lambda << d
• Wave Optics: \lambda > d

Superposition and Interference

• Waves in phase: Constructive interference.
• Waves out of phase: Destructive interference.

Young's Double Slit Experiment

• Shows interference effects of light.
• Measures wavelength of light.

Single Slit Diffraction

• Condition for minima: $D \sin\theta = m \lambda$
• Approximation for small angles: $y = \frac{m \lambda L}{D}$

Single Slit Examples

• First minimum angle: $\sin\theta = \frac{\lambda}{D}$
• Minimum slit width: $D = \frac{\lambda}{\sin\theta}$