Light: Reflection and Refraction
In one line
Light bounces off shiny surfaces (reflection) and bends when it passes from one material into another (refraction), and mirrors and lenses use this to form images.
Reflection
- First law: the angle of incidence equals the angle of reflection (∠i = ∠r).
- Second law: the incident ray, the reflected ray and the normal all lie in the same plane.
- A plane mirror forms an image that is virtual, upright, the same size, and as far behind the mirror as the object is in front. Left and right are swapped.
- Concave mirror (curves inward): converges light. Used in torches, headlights, shaving and dentist mirrors.
- Convex mirror (bulges outward): always gives a small, upright, virtual image with a wide view. Used as rear-view mirrors in vehicles.
1/v + 1/u = 1/f · f = R/2 · m = h′/h = −v/u
Sign convention (New Cartesian)
- Measure all distances from the pole of the mirror or the optical centre of the lens.
- Distances in the direction of incoming light are positive; against it, negative. The object is usually on the left, so u is negative.
- Heights above the principal axis are positive, below are negative.
- Concave mirror: f is negative. Convex mirror: f is positive. Convex lens: f positive. Concave lens: f negative.
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Refraction
- Light bends because its speed changes in a different material.
- Going into a denser medium (air → glass), light bends towards the normal. Coming out, it bends away.
- Snell's law: sin i / sin r = constant, the refractive index.
- Refractive index n = speed of light in vacuum ÷ speed in the medium. Water ≈ 1.33, glass ≈ 1.5, diamond ≈ 2.42.
- A pencil in water looks bent, and a pool looks shallower than it is, because of refraction.
Lens: 1/v − 1/u = 1/f · m = v/u · P = 1/f (f in metres)
Power is measured in dioptres (D). A convex lens has positive power, a concave lens negative power.
Solved examples
1. Concave mirrorAn object is 30 cm in front of a concave mirror with f = 15 cm. So u = −30, f = −15.
1/v = 1/f − 1/u = −1/15 + 1/30 = −1/30, so v = −30 cm. The image is real, inverted, the same size, 30 cm in front of the mirror. m = −v/u = −1.
1/v = 1/f − 1/u = −1/15 + 1/30 = −1/30, so v = −30 cm. The image is real, inverted, the same size, 30 cm in front of the mirror. m = −v/u = −1.
2. Power of a lensA convex lens has f = 50 cm = 0.5 m. P = 1/0.5 = +2 D.
3. Speed in glassn = 1.5. Speed in glass = 3 × 10⁸ ÷ 1.5 = 2 × 10⁸ m/s.
Common mistakes
- Using the mirror formula for lenses. Mirror: 1/v + 1/u. Lens: 1/v − 1/u.
- Forgetting the minus sign on u. With the object on the left, u is negative.
- Power in centimetres. Change f to metres before working out P = 1/f.
Quick check
Revise in 30 seconds
| Reflection | ∠i = ∠r; rays and normal in one plane |
|---|---|
| Mirror formula | 1/v + 1/u = 1/f; f = R/2; m = −v/u |
| Lens formula | 1/v − 1/u = 1/f; m = v/u |
| Refractive index | n = c/v = sin i / sin r |
| Power | P = 1/f (metres), unit dioptre |
| Uses | Concave: torch, shaving · Convex mirror: rear view · Convex lens: magnifier |