The angle of incidence equals the angle of reflection: θᵢ = θᵣ. Both angles are measured from the normal to the surface.
Image is virtual, upright, same size, and located the same distance behind the mirror as the object is in front. Laterally inverted (left-right swap).
Concave (converging): f = R/2 (positive). Convex (diverging): f = −R/2 (negative). Mirror equation: 1/f = 1/dᵢ + 1/dₒ. Magnification: m = −dₒ/dᵢ. Real images: dₒ > 0 (inverted). Virtual images: dₒ < 0 (upright).
Two kinds of aberration. Spherical aberration is the blurring that happens because a spherically curved mirror or lens does not bring rays far from the axis to the same focus as rays near it; it is reduced by using only a narrow beam near the axis, or by using a parabolic mirror, which focuses all parallel rays to a single point. Chromatic aberration is a lens-only fault: the refractive index depends on wavelength, so blue light is bent more than red and each colour focuses at a different distance, fringing the image. Mirrors do not suffer from it at all, since reflection does not disperse — which is why large telescopes use mirrors.
Brewster's angle. When unpolarised light strikes a surface at the angle where the reflected and refracted rays would be perpendicular to each other, the reflected light is completely plane-polarised. That angle satisfies tan θ_B = n₂/n₁, and it is why polarising sunglasses cut the glare from water and roads: the reflected light is already polarised in one plane, so a filter turned across it removes almost all of it.
💡θᵢ = θᵣ. Mirror equation: 1/f = 1/dᵢ + 1/dₒ. m = −dₒ/dᵢ. Sign conventions are critical.
📋 Key Formulas
📝 Worked Example 1
Q: Object 30 cm from concave mirror, f = 20 cm. Image location and type?
A: 1/20 = 1/30 + 1/dₒ → 1/dₒ = 1/20 − 1/30 = 1/60 → dₒ = 60 cm. Real, inverted, m = −60/30 = −2 (enlarged).
📝 Worked Example 2
Q: Object 10 cm from concave mirror, f = 20 cm. Image?
A: 1/20 = 1/10 + 1/dₒ → 1/dₒ = 1/20 − 1/10 = −1/20 → dₒ = −20 cm. Virtual, upright, m = 2.
📝 Worked Example 3
Q: Convex mirror f = −15 cm, object 30 cm away. Image?
A: 1/(−15) = 1/30 + 1/dₒ → dₒ = −10 cm. Virtual, upright, m = 1/3 (diminished).
🧠Follow sign conventions strictly.
🧠Draw ray diagrams to verify.
🧠Convex mirrors always give virtual, diminished images.
⚠️Wrong sign for f in convex mirrors.
⚠️Forgetting the negative in m = −dₒ/dᵢ.
⚠️Not checking if image is real or virtual.
🎯 Try This Yourself
Open and read all sections to complete this module