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Ray Optics

Grown into a cornerstone. Mirrors, refraction, lenses and prisms each come down to one equation used with a fixed sign convention, so the convention is half the chapter.

Questions in the bank
169
q/paper in 2025–26
2.02
Numeric answer
30%
Notes pages
8

Tier: Cornerstone

When you’ll see it

A mirror, a lens, a slab, a prism or a curved glass surface, and the question asks where the image forms, how big it is, or how a ray bends.

How this chapter is tested

This is a cornerstone chapter, and it has grown a great deal since the early papers. Nearly every question is solved with the mirror formula, the lens formula or Snell's law, applied with one sign convention throughout: Cartesian, with distances measured from the pole or the optical centre and taken positive in the direction the light travels.

Lenses are the biggest single part: the lens formula, combinations, a lens in a liquid, cut lenses and silvered lenses. Mirrors, refraction at flat and curved surfaces, total internal reflection and prisms make up most of the rest, and optical instruments close the chapter.

Marks are lost on a sign rather than on the physics: a concave mirror's focal length taken as positive, a virtual object given a negative distance, or a curved face's radius written with the wrong sign. Draw the light's direction before writing any distance. Resolving power is shared with Wave Optics.

The sub-skills

The distinct skills inside the chapter, in the order to learn them.

  • Plane and spherical mirrors

    1/v + 1/u = 1/f with f = R/2 and m = −v/u; a plane mirror gives an erect, same-size image, and along the axis the image speed scales with m².

  • Refraction at flat surfaces

    n₁ sin i = n₂ sin r with angles from the normal; a slab shifts a ray sideways without turning it, and an object under a liquid looks d/μ deep.

  • Critical angle and total internal reflection

    sin C = n(rarer)/n(denser); total reflection needs light starting in the denser medium at more than C, and the bright circle above a lamp has radius h tan C.

  • One curved surface and the lens-maker's formula

    μ₂/v − μ₁/u = (μ₂ − μ₁)/R, with the sign of R set by where the centre is; two such surfaces give 1/f = (μ − 1)(1/R₁ − 1/R₂).

  • Thin lenses and combinations

    1/v − 1/u = 1/f with m = v/u; powers add in contact, and separated lenses are solved one after another, each image becoming the next object.

  • Lenses in a liquid, cut and silvered

    Power scales with μ(lens)/μ(medium) − 1; a cut along the axis keeps the focal length, a cut across it doubles it; a silvered lens is a mirror of power 2P(lens) plus that of the silvered face.

  • Prisms

    r₁ + r₂ = A and deviation i + e − A; at minimum deviation μ = sin((A + δm)/2)/sin(A/2); a thin prism deviates by (μ − 1)A, and red bends least.

  • Optical instruments and the eye

    Microscope (L/fₒ)(D/fₑ) and telescope fₒ/fₑ in normal adjustment; resolving power grows with the aperture and falls with the wavelength; each defect of vision has its own lens.

Traps to expect

Distractor shapes this chapter reuses. The Traps page covers the ones that cut across chapters.

  • Mirror and lens formulas swapped

    A mirror uses 1/v + 1/u = 1/f with m = −v/u; a lens uses 1/v − 1/u = 1/f with m = v/u. Mixing them flips a sign or the nature of the image.

  • The sign of a radius

    A concave face met from outside has its centre on the incoming side, so R is negative, and R₂ of a biconvex lens is negative. Writing every radius as positive makes the focal length far too long.

  • A virtual object has u > 0

    When the first image lies beyond the second lens, the object for that lens is on its outgoing side. Measure from the second lens, not the first.

  • Angle from the surface

    A ray at 30° with the surface has an angle of incidence of 60°. Snell's law and the critical angle both take angles from the normal.

Learn it before you drill it

This chapter has full teaching notes — foundations, worked examples, self-checks and a mastery check for each page. Read the notes once, then drill page by page below.

Ray Optics notes

Drill every Ray Optics question

169 questions from the bank, across 8 subtopics.

Drill the 169 questions

Drill one subtopic at a time

The 8 subtopics, in teaching order.

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