Optics
Optics spans ray optics (mirrors, lenses, prisms) and wave optics (interference, diffraction, polarization). The exam asks for sign-convention numericals, the lens maker's formula and a Young's double-slit calculation.
Core rules
- Refraction: n = c/v = sin i/sin r, and n₁ sin i = n₂ sin r. Apparent depth = real depth/n.
- Total internal reflection needs light travelling from denser to rarer medium and i greater than the critical angle, with sin C = 1/n.
- Sign convention: distances measured from the pole or optical centre, positive along the incident light. Mirror: 1/f = 1/v + 1/u. Lens: 1/f = 1/v − 1/u.
- Lens maker: 1/f = (n − 1)(1/R₁ − 1/R₂). Power P = 1/f with f in metres, in dioptres; thin lenses in contact add: P = P₁ + P₂.
- Prism: A + δ = i + e; at minimum deviation n = sin((A + D)/2)/sin(A/2).
- YDSE: fringe width β = λD/d; bright fringes at path difference nλ, dark at (2n − 1)λ/2.
- Diffraction and polarization confirm wave nature; Brewster's law tan θ_p = n.
Worked example
In YDSE, λ = 600 nm, slit separation d = 0.50 mm and screen distance D = 1.0 m. Find the fringe width. β = λD/d = (600×10⁻⁹ × 1.0)/(0.50×10⁻³) = 1.2×10⁻³ m = 1.2 mm. Convert nm and mm to metres before dividing; the result is the separation between successive bright or successive dark fringes.
Traps
Dropping the sign convention and calling a virtual image real; forgetting that β shrinks by a factor n when the apparatus is immersed in a liquid; writing power as 1/f with f in cm; mixing the mirror and lens formulae; and assuming diffraction fringes are equally spaced like YDSE fringes.