Optics
Optics tests ray optics of mirrors and lenses, refraction and total internal reflection, optical instruments, and wave optics including interference, diffraction, and polarisation. The exam expects correct sign conventions and clear distinction between ray and wave phenomena.
Core rules and concepts
- Mirror formula: 1/v + 1/u = 1/f. Lens formula: 1/v - 1/u = 1/f, with Cartesian sign convention. Magnification m = v/u for mirrors and m = v/u for lenses with signs.
- Refraction: n1 sin(theta1) = n2 sin(theta2). Refractive index n = c/v. Total internal reflection occurs from denser to rarer medium when the angle exceeds sin^-1(1/n).
- Lens maker formula: 1/f = (n - 1)(1/R1 - 1/R2). Power in dioptres is P = 1/f(m).
- Young double-slit fringe width beta = lambda D/d. Constructive path difference = n lambda; destructive = (n + 1/2)lambda.
- Single-slit diffraction has central maximum width proportional to lambda/a. Polarisation shows light is transverse; Brewster law tan(theta_p) = n.
Worked example
A convex lens of focal length 20 cm forms an image of an object 30 cm in front. Using 1/v - 1/u = 1/f with u = -30 cm and f = +20 cm: 1/v + 1/30 = 1/20, so 1/v = 1/60 and v = +60 cm. Magnification m = v/u = 60/(-30) = -2: the image is real, inverted, and twice the object size.
Traps that cost marks
- Using the mirror formula for a lens or ignoring Cartesian signs.
- Applying TIR from rarer to denser medium.
- Confusing fringe width dependence on D and d.
- Treating diffraction and interference as identical.
- Forgetting that power in dioptres uses focal length in metres.