Ray Optics and Optical Instruments
What is examined
Ray Optics and Optical Instruments tests reflection at spherical mirrors, refraction, total internal reflection, the lens maker's formula, thin lenses, power, prisms, dispersion and the working of microscopes and telescopes.
Core rules
- Mirror formula 1/v + 1/u = 1/f, with f = R/2; magnification m = −v/u.
- Snell's law n₁ sin i = n₂ sin r; n = c/v. Total internal reflection occurs only from denser to rarer medium, when i exceeds the critical angle C with sin C = 1/n.
- Lens maker: 1/f = (n − 1)(1/R₁ − 1/R₂). Thin lens: 1/v − 1/u = 1/f; m = v/u.
- Power in dioptres: P = 1/f with f in metres; powers of thin lenses in contact add.
- Prism: A + δ = i + e; at minimum deviation r = A/2 and n = sin[(A + δ_m)/2]/sin(A/2). Dispersion arises because n decreases with wavelength.
- Compound microscope: M ≈ (v₀/u₀)(D/f_e), objective of small focal length. Telescope: M = f₀/f_e in normal adjustment; objective of large diameter for light gathering.
Worked example
An object is 30 cm from a convex lens of focal length 20 cm. Find image position and magnification. Using 1/v − 1/u = 1/f with u = −30 cm, f = +20 cm: 1/v = 1/20 + 1/(−30) = 1/60, so v = +60 cm. The image is real and on the other side. m = v/u = 60/(−30) = −2: inverted and twice the size.
Traps
Ignoring sign convention; writing P = 1/f with f in cm; expecting TIR from rarer to denser; and mixing up the microscope and telescope magnification formulas.