Light — Reflection and Refraction
AI-assisted · review in progress · last updated 25 July 2026 · jump to quick revision
In 30 seconds
- Light travels in straight lines; it reflects off polished surfaces and bends (refracts) when it changes medium.
- Two laws of reflection: angle of incidence = angle of reflection, and the incident ray, reflected ray and normal lie in one plane.
- One mirror formula and one lens formula carry most of the numericals — plus magnification.
- Refraction is governed by refractive index; Snell's law links the angles of incidence and refraction.
- The sign convention decides every answer's sign — get it right and the rest is arithmetic.
Reflection of light
A polished surface like a mirror sends light back into the same medium instead of absorbing it. This bouncing back is reflection, and it follows two simple laws that hold for every mirror — plane or curved.
- The angle of incidence is equal to the angle of reflection (∠i = ∠r).
- The incident ray, the reflected ray and the normal at the point of incidence all lie in the same plane.
- A plane mirror forms a virtual, erect image, the same size as the object, as far behind the mirror as the object is in front of it, and laterally inverted.
Angles are always measured from the normal — the perpendicular to the surface at the point where the ray strikes — never from the mirror surface itself.
Spherical mirrors
A spherical mirror is a piece of a hollow sphere. If the reflecting surface curves inwards it is a concave mirror (converging); if it bulges outwards it is a convex mirror (diverging).
Principal focus (F)
The point on the principal axis where rays parallel to the axis actually meet after reflection (concave mirror), or appear to come from (convex mirror). The distance from the pole to this point is the focal length f, and it is half the radius of curvature: R = 2f.
The New Cartesian sign convention makes the formulas work: all distances are measured from the pole, distances in the direction of the incident light are positive, distances against it are negative, and heights above the principal axis are positive. In practice: the object distance u is negative, a concave mirror has negative f, and a convex mirror has positive f.
When to use: any numerical with a spherical mirror — two of u, v, f given, find the third; magnification for size/nature of image
Reading the magnification: if m is negative the image is real and inverted; positive means virtual and erect. |m| > 1 means enlarged, |m| < 1 means diminished.
An object is placed 20 cm in front of a concave mirror of focal length 15 cm. Find the position and nature of the image.
With the sign convention, u = −20 cm and f = −15 cm.
So v = −60 cm. The magnification is m = −v/u = −(−60)/(−20) = −3: real, inverted, three times the object’s size.
Answer: v = −60 cm: a real, inverted image 60 cm in front of the mirror, magnified 3×.
Where images form (concave mirror): object beyond C → image between C and F (real, diminished); at C → at C (real, same size); between C and F → beyond C (real, magnified); between F and P → behind the mirror (virtual, erect, magnified — the shaving-mirror case). A convex mirror always gives a virtual, erect, diminished image — which is why it’s used as a rear-view mirror: a wide field of view, always upright.
Refraction of light
When light passes from one transparent medium into another, its speed changes, so the ray bends at the boundary. This is refraction. Going from a rarer to a denser medium (air → glass) the ray bends towards the normal; denser to rarer, away from it.
Refractive index (n)
The refractive index of medium 2 with respect to medium 1 is the ratio of the speed of light in medium 1 to its speed in medium 2: n₂₁ = v₁/v₂. With respect to vacuum, n = c/v — always ≥ 1; the larger it is, the optically denser the medium.
When to use: the angles at a boundary are involved
- A rectangular glass slab bends the ray twice, in opposite directions: the emergent ray is parallel to the incident ray, just shifted sideways (lateral displacement).
- A ray striking the boundary along the normal (∠i = 0) passes straight through, undeviated.
- Everyday signs of refraction: a pencil looks bent in a glass of water, a pool looks shallower than it is.
Lenses and power
A lens refracts light twice, once at each surface. A convex lens is thicker in the middle and converges light; a concave lens is thinner in the middle and diverges it. For lenses the sign convention gives a convex lens positive f and a concave lens negative f — the opposite pairing to mirrors, which is where many marks are lost.
When to use: any numerical with a lens — note the minus sign: it is 1/v − 1/u, unlike the mirror formula
Power of a lens (P)
The reciprocal of the focal length expressed in metres: P = 1/f. Its SI unit is the dioptre (D). Convex lenses have positive power, concave negative. For thin lenses in contact, powers simply add: P = P₁ + P₂ + …
A lens has a focal length of −25 cm. What is its power, and what kind of lens is it?
Convert to metres: f = −0.25 m. Then P = 1/f = 1/(−0.25) = −4 D.
Answer: P = −4 D; the negative power means it is a concave (diverging) lens.
- Using the mirror formula for a lens or vice versa — the lens formula has a minus sign (1/v − 1/u), the mirror formula a plus.
- Forgetting to convert focal length to metres before computing power.
- Dropping the sign of u: for a real object u is negative in every standard numerical.
- Mixing up the magnification formulas: m = −v/u for mirrors but m = v/u for lenses.
- Measuring angles from the surface instead of from the normal.
Quick revision cards
Laws of reflection?
Mirror formula?
Lens formula?
Relation between R and f?
Snell's law?
Power of a lens?
Which mirror is used as a rear-view mirror, and why?
What does negative magnification tell you?