Optics & Waves
Welcome to Optics & Waves! This module covers reflection, refraction, lenses, interference, diffraction and the properties of waves, plus vibrations and mechanical waves. The photoelectric effect, atomic spectra and nuclear physics have their own Modern Physics module.
What the Exam Tests
The syllabus's Optics module has two topics: geometrical optics (the laws of reflection and refraction) and physical optics (interference and diffraction). This module teaches them, with lenses and the properties of waves. Curved mirrors and lenses (the mirror and lens equations), Brewster’s angle, Malus’s law, diffraction gratings and the single-slit formula, and string and pipe harmonics go beyond the syllabus and are background. It also holds Vibrations & Waves, which the syllabus lists under Mechanics.
Questions can ask you to trace a ray through a prism or a glass block, find a refractive index or a critical angle, compare two colours of light, or use Δx = Lλ/d for double-slit fringes.
In our mock papers Optics gets 5 of the 48 questions. The CSCA publishes the topics but not how many questions each gets, so this split is our own reading of the syllabus. The photoelectric effect, atomic structure and nuclear physics are in the Modern Physics module.
Law of Reflection
The angle of incidence equals the angle of reflection: θᵢ = θᵣ. Both angles are measured from the normal to the surface.
Plane Mirrors
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).
The full law of reflection (光的反射定律): the reflected ray, the incident ray and the normal lie in one plane, with the two rays on opposite sides of the normal (反射光线、入射光线与法线在同一平面内，反射光线与入射光线分别位于法线两侧，反射角等于入射角). A useful consequence: if a plane mirror turns through an angle α while the incident ray stays fixed, the reflected ray turns through 2α.
Curved Mirrors
Beyond the syllabus: the CSCA syllabus lists only the laws of reflection and refraction for geometrical optics. Curved mirrors, the mirror equation, aberrations and Brewster’s angle below are background, not required.
Concave (converging): f = R/2 (positive). Convex (diverging): f = −R/2 (negative). Mirror equation: 1/f = 1/dᵢ + 1/dₒ. Magnification: m = −dᵢ/dₒ. Real images: dᵢ > 0 (inverted). Virtual images: dᵢ < 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 θB = 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.
Key takeaway: θᵢ = θᵣ, both measured from the normal; a plane mirror gives a virtual, upright, same-size image as far behind the mirror as the object is in front. Background beyond the syllabus: mirror equation 1/f = 1/dᵢ + 1/dₒ, m = −dᵢ/dₒ.
Key Formulas
- θᵢ = θᵣ
- 1/f = 1/dᵢ + 1/dₒ
- m = −dᵢ/dₒ, f = R/2
Worked Example 1
Q: Object 30 cm from concave mirror, f = 20 cm. Image location and type?
A: dₒ = 30 cm, so 1/20 = 1/30 + 1/dᵢ → 1/dᵢ = 1/20 − 1/30 = 1/60 → dᵢ = 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/dᵢ → 1/dᵢ = 1/20 − 1/10 = −1/20 → dᵢ = −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/dᵢ → 1/dᵢ = −1/15 − 1/30 = −1/10 → dᵢ = −10 cm. Virtual, upright, m = 1/3 (diminished).
Exam tip: Follow sign conventions strictly.
Exam tip: Draw ray diagrams to verify.
Exam tip: Convex mirrors always give virtual, diminished images.
Common mistake: Wrong sign for f in convex mirrors.
Common mistake: Forgetting the negative in m = −dᵢ/dₒ.
Common mistake: Not checking if image is real or virtual.
Try This Yourself
Module Summary
You have completed Optics & Waves! Key topics: reflection, refraction and total internal reflection, lenses, interference, diffraction, wave properties, and vibrations and mechanical waves. Modern physics continues in its own module.
Open and read all sections to complete this module