Optics (Ray Optics and Wave Optics)
What the exam tests
Ray optics questions cover mirrors, lenses, refraction, total internal reflection, prisms, optical instruments and power. Wave optics covers Huygens principle, Young double-slit interference, diffraction, polarization and resolution.
Core rules
- Mirror formula 1/f = 1/v + 1/u with sign convention; lens formula 1/f = 1/v − 1/u. Power P = 1/f in dioptres when f is in metres.
- Refraction: n1 sin i = n2 sin r. Total internal reflection needs n1 > n2 and i greater than critical angle C, where sin C = n2/n1.
- Thin lenses in contact: P = P1 + P2.
- Young double-slit fringe width β = λD/d. Bright fringes occur for path difference nλ; dark for (n + 1/2)λ.
- Single-slit diffraction minima: a sinθ = nλ.
- Polarization shows the transverse nature of light; Malus law gives I = I0 cos^2θ for analyser angle θ.
Worked example
A convex lens of focal length 20 cm forms an image of an object 30 cm away. Using 1/f = 1/v − 1/u with u = −30 cm and f = +20 cm, 1/v = 1/20 + 1/(−30) = 1/60. Thus v = +60 cm. The positive sign means a real image on the opposite side. Magnification m = v/u = 60/(−30) = −2, so the image is inverted and twice the object size.
Traps
Sign convention errors cause most lost marks. A virtual image has a negative image distance for a lens. Fringe width increases with D and λ and decreases with slit separation d; it changes when the apparatus is immersed in water because λ decreases. Diffraction is not the same as interference. Critical angle exists only when light travels from denser to rarer medium.