Optics: Ray Optics and Optical Instruments; Wave Optics
Optics combines ray treatment of mirrors, lenses and instruments with wave treatment of interference, diffraction and polarisation. Numerical questions often turn on sign convention and coherence.
Core rules and concepts
- Mirror formula 1/v + 1/u = 1/f; lens formula 1/v − 1/u = 1/f. Magnification m = v/u for mirrors and m = v/u for lenses with the Cartesian sign convention.
- Refraction: n1 sin i = n2 sin r. Total internal reflection needs n1 > n2 and i > critical angle C, where sin C = n2/n1.
- Lens power P = 1/f (f in metres), measured in dioptres. A compound microscope magnifies small nearby objects; a telescope magnifies distant objects.
- Young’s double-slit fringe width β = λD/d. Constructive interference occurs when path difference = nλ; destructive when (n + ½)λ.
- Diffraction at a single slit gives minima at a sinθ = nλ. Polarisation shows light is transverse; a polariser can reduce intensity.
Worked example
In Young’s experiment, λ = 600 nm, slit separation d = 0.5 mm and screen distance D = 1 m. Find fringe width. β = λD/d = (600×10⁻⁹)(1)/(0.5×10⁻³) = 1.2×10⁻³ m = 1.2 mm.
Traps
- Use one sign convention consistently; mixing real-is-positive and Cartesian signs ruins lens problems.
- Total internal reflection cannot occur from rarer to denser medium.
- Fringe width increases with λ and D, but decreases with slit separation d.
- Interference needs coherent sources; two independent lamps do not give a stable pattern.
- Diffraction and interference are distinct; single-slit minima are not double-slit fringes.