Optics
Optics questions test reflection, refraction, total internal reflection, thin lenses and mirrors, and the wave phenomena of interference and diffraction.
Core rules
- Reflection: angle of incidence equals angle of reflection, measured from the normal.
- Snell's law: n₁ sinθ₁ = n₂ sinθ₂, with n = c/v. Light bends toward the normal entering a denser medium.
- Total internal reflection requires n₁ > n₂ and θ₁ > θ_c, where sinθ_c = n₂/n₁.
- Thin lens: 1/f = 1/u + 1/v with a consistent sign convention; magnification m = −v/u = h_i/h_o. A positive v means a real image on the opposite side for a converging lens.
- Young's double slit: fringe spacing Δx = λL/d.
- Diffraction grating: d sinθ = mλ, where d is the slit spacing.
- In glass, shorter wavelengths have larger n, so blue bends more than red.
Worked example
An object is 30 cm from a converging lens of focal length 10 cm. Using 1/v = 1/f − 1/u = 1/10 − 1/30 = 1/15, so v = 15 cm. The image is real, on the far side, and m = −15/30 = −0.5: inverted and half the object height.
Traps
Mixing sign conventions mid-calculation; using degrees when the calculator is in radian mode; forgetting that wavelength changes but frequency does not on refraction; calling a virtual image real because v is positive under a different convention; mixing centimetres and metres in Δx = λL/d.