Optics
Optics
This domain covers reflection at plane and spherical mirrors, refraction through lenses and glass, image formation, refractive index, total internal reflection and simple dispersion. The exam favours ray-diagram reasoning expressed in words and formula-based numericals.
Core rules
- Laws of reflection: angle of incidence equals angle of reflection; incident ray, reflected ray and normal lie in one plane.
- Mirror formula: 1/f = 1/v + 1/u, with sign convention. Concave mirror f is negative; convex mirror f is positive.
- Lens formula: 1/f = 1/v − 1/u. Convex lens f is positive; concave lens f is negative.
- Magnification: m = h′/h = v/u for a lens and m = −v/u for a mirror.
- Refractive index n = speed of light in vacuum / speed in medium = c/v.
- Total internal reflection occurs when light travels from denser to rarer medium and incidence angle exceeds critical angle.
- Power of a lens P = 1/f in dioptre when f is in metres.
Worked example
An object is 20 cm from a concave mirror of focal length 10 cm. Taking u = −20 cm and f = −10 cm: 1/v = 1/f − 1/u = −1/10 + 1/20 = −1/20, so v = −20 cm. The image is real, inverted and 20 cm in front of the mirror. Magnification m = −v/u = −(−20)/(−20) = −1, so it is same size.
Traps
Sign errors dominate. Convert cm to m for power. A real image is inverted for a single lens or mirror; a virtual image is erect. Do not use lens formula for mirrors. For TIR, both conditions-denser to rarer and angle above critical-must be met.