Exercise Solutions Available
Step-by-step answers for all textbook questions in this chapter
Overview
Ray optics treats light as straight-line rays to explain reflection, refraction, mirrors, lenses, prisms, and total internal reflection.
1. Reflection & Mirror Formula
1/v + 1/u = 1/f (f = R/2 for spherical mirrors)
Magnification: m = −v/u = h_image/h_object
Sign convention: distances measured from pole, against incident light are negative.
2. Refraction
Snell's law: n₁ sin i = n₂ sin r
Refractive index: n = c/v = real depth/apparent depth
Total internal reflection: sin C = 1/n (denser → rarer, angle > C)
3. Lenses and Prism
Lens formula: 1/v − 1/u = 1/f
Lens maker: 1/f = (n − 1)(1/R₁ − 1/R₂)
Power: P = 1/f (in metres), unit dioptre (D)
Prism: n = sin[(A + Dₘ)/2] / sin(A/2)
Worked Examples
Example 1 — Mirror formula
Object 30 cm from a concave mirror of f = 10 cm (f negative). Find v.
1/v + 1/u = 1/f → 1/v + 1/(−30) = 1/(−10)
1/v = −1/10 + 1/30 = −2/30 → v = −15 cm (real, in front)
Example 2 — Magnification
For the above, find magnification.
m = −v/u = −(−15)/(−30) = −0.5 (real, inverted, half size)
Example 3 — Critical angle
Critical angle for glass of n = 1.5.
sin C = 1/n = 1/1.5 = 0.667 → C = 41.8°
Example 4 — Lens power
A convex lens has f = 20 cm. Find its power.
P = 1/f(m) = 1/0.20 = +5 D
Common Mistakes
- Ignoring the sign convention (concave f negative, convex f positive).
- Lens formula is 1/v − 1/u (not +) unlike the mirror formula.
- Forgetting f = R/2 for mirrors.
- Using degrees/centimetres inconsistently with power (needs metres).
Exam Tips & Revision Checklist
- Mirror: 1/v + 1/u = 1/f ; Lens: 1/v − 1/u = 1/f — note the sign difference.
- sin C = 1/n is the quick TIR test.
- Practised: mirror formula, magnification, critical angle, lens power.
Frequently Asked Questions
1/v + 1/u = 1/f, where u is object distance, v image distance, and f focal length (sign convention applies).