Optics: Geometric Optics, Lenses and Mirrors, Interference and Diffraction
Optics splits into two exam styles: ray problems on mirrors and lenses, where sign conventions decide everything, and wave problems on interference and diffraction, where a single formula and careful unit conversion give the answer. Expect one construction or calculation with a lens and one quantitative treatment of a double slit or grating.
Reflection and refraction
Angle of incidence equals angle of reflection, both measured from the normal. Refraction obeys Snell's law, n₁ sin θ₁ = n₂ sin θ₂, with n = c/v. Light bending toward the normal means it entered a denser medium. Total internal reflection occurs only when travelling from denser to less dense and only beyond the critical angle, sin θ_c = n₂/n₁. Shorter wavelengths refract more, which is why a prism disperses white light.
Lenses and mirrors
Use 1/f = 1/u + 1/v together with magnification m = v/u (or −v/u in the Cartesian convention), and state your convention explicitly. For a converging lens f is positive; a diverging lens has f < 0. A real image is formed on the opposite side of a lens and can be caught on a screen; a virtual image cannot. Lens power in dioptres is P = 1/f with f in metres. For mirrors, f = R/2.
Wave optics
Young's double slit gives fringe spacing w = λD/a, where a is the slit separation and D the slit-to-screen distance. The nth bright fringe sits at y = nλD/a, so fringe spacing is the distance between neighbouring fringes, not to the nth one. A diffraction grating obeys d sin θ = nλ, with d the line spacing (1/lines per metre). Single-slit diffraction broadens the central maximum; polarisation proves light is transverse.
Worked example
An object is placed 30 cm from a converging lens of focal length 10 cm. Locate and describe the image. 1/f = 1/u + 1/v gives 1/10 = 1/30 + 1/v, so 1/v = 1/10 − 1/30 = 1/15 and v = 15 cm. Since v is positive the image is real, formed 15 cm on the far side of the lens. Magnification m = v/u = 15/30 = 0.5, so the image is half-size and inverted.
Traps that cost marks
- Mixing conventions mid-question; choose real-is-positive or Cartesian and keep it throughout.
- Applying the critical-angle formula when light goes from less dense to denser.
- Using the slit width instead of the slit separation a in w = λD/a.
- Leaving λ in nanometres or D in centimetres before dividing.
- Reporting the position of the nth fringe when the spacing between fringes was requested.