Press ▶ and the lecture reads itself to you while the panel on the right shows every idea through an everyday object you already know — a car's convex mirror, a straw bent in a glass, the PTCL fibre on your street, a pair of spectacles, a magnifying glass, a glittering diamond. Light as rays: reflection and mirrors, Snell's law, total internal reflection, lenses and the eye.
1 — Reflection, plane & convex mirrors
When light strikes a polished surface it reflects, obeying the laws of reflection — both angles measured from the normal, never from the surface.
Laws of reflection1. incident ray, reflected ray & normal lie in one plane
2. ∠i = ∠r — always, measured from the normal
- Plane mirror — image is virtual, erect, same size, as far behind as the object is in front (q = p), and laterally inverted. That is why AMBULANCE is mirror-painted on the bonnet.
- Convex mirror — bulges towards you, diverges light, and always gives a small, erect, virtual image with a huge field of view — the side mirror that warns "objects are closer than they appear".
worked — rear-view convex mirror
A car 4.0 m behind a convex mirror, f = −1.0 m.
1/q = 1/(−1.0) − 1/4.0 = −1.25 → q = −0.8 m · m = 0.8/4.0 = 0.2 — virtual, erect, ⅕ size
Real world: convex → vehicle & shop-corner mirrors; concave → shaving, dentist and headlight mirrors.
2 — Refraction, Snell's law & apparent depth
Crossing into a new medium light changes speed and bends — refraction. Into a denser medium (air → glass/water) it bends towards the normal; into a rarer one, away.
Snell's law & refractive indexn = sin i / sin r = c / v
n(water) = 1.33 · n(glass) ≈ 1.5 · n(diamond) = 2.42 · n has no unit
Because rays from underwater bend away at the surface, the eye traces them back to a raised point — the straw looks snapped, the pool looks shallow, the coin floats up.
Apparent depthn = real depth / apparent depth → apparent = real / n
worked — measuring n & the pool
A ray refracts 45° → 28° in glass; a pool is 2.0 m deep (n = 1.33).
n = sin45°/sin28° = 0.707/0.469 = 1.51 · apparent depth = 2.0/1.33 = 1.5 m
3 — Total internal reflection & the optical fibre
Going from a denser to a rarer medium the ray bends away from the normal. At the critical angle C the refracted ray skims the surface (r = 90°); beyond C nothing escapes — total internal reflection (TIR), a perfect mirror with no silvering.
Critical anglesin C = 1/n
glass → 41.8° · water → 48.8° · diamond → 24.4°
- Two conditions for TIR — (1) denser → rarer medium; (2) angle of incidence > C.
- Optical fibre — light trapped by repeated TIR carries your PTCL fibre internet and the surgeon's endoscope with almost no loss.
- Mirage — sky-rays TIR off hot rare air above the road, which gleams like water.
worked — water–air critical angle
n = 1.33; a ray hits the surface from below at 55°.
sin C = 1/1.33 = 0.752 → C = 48.8° · 55° > 48.8° → total internal reflection
4 — The eye & its defects
The eye is a living camera: cornea and lens form a real, inverted image on the retina; the ciliary muscles refocus the lens — accommodation. A normal eye sees from the near point ≈ 25 cm to the far point at infinity.
| Defect | Image lands | Correcting lens |
|---|
| myopia (short sight) | before the retina | concave (P negative) |
| hypermetropia (long sight) | behind the retina | convex (P positive) |
worked — prescribing spectacles
A myopic eye sees clearly only to 2.0 m.
lens must image infinity at 2.0 m → f = −2.0 m → P = 1/f = −0.5 D (concave)
Memory hook: myopia = "near is okay" → minus (concave) lens; hypermetropia = "far is okay" → plus (convex) lens.
5 — Lenses, the lens formula & the magnifier
A convex lens converges light, a concave lens diverges it. The same formula as mirrors finds the image, and opticians grade lenses by power in dioptres.
Lens formula & power1/f = 1/p + 1/q · m = q/p
P = 1/f(metres) → dioptre (D) · convex +, concave −
With the object within f the image is virtual, erect and magnified — that is the magnifying glass:
Angular magnification of a magnifierM = 1 + d/f (d = 25 cm) · shorter f → more magnification
worked — projector & reading lens
(a) p = 30 cm, convex f = 20 cm. (b) a 5 cm reading lens.
(a) 1/q = 1/20 − 1/30 = 1/60 → q = 60 cm · m = 2 · P = +5 D · (b) M = 1 + 25/5 = 6×
6 — Dispersion, the prism & diamond fire
A glass prism bends violet light more than red because n is slightly larger for shorter wavelengths — white light fans out into the spectrum. This dispersion is how a raindrop paints a rainbow.
- Diamond's fire — with C only 24.4°, almost any ray entering a cut diamond is trapped by repeated TIR and bursts out flashing — its famous sparkle.
- Reflecting prisms — a 45°–45°–90° prism turns light by 90° or 180° using TIR, beating any silvered mirror (periscopes, binoculars).
worked — why diamonds sparkle
n of diamond = 2.42.
sin C = 1/2.42 = 0.413 → C = 24.4° — almost every internal ray is totally reflected.
7 — Spherical mirrors & the mirror formula
A concave mirror converges light. The focus sits halfway to the centre of curvature: f = R/2. Two rays locate any image: a parallel ray reflects through F; a ray through C reflects back on itself.
Mirror formula & magnification1/f = 1/p + 1/q · m = q/p
f = R/2 · concave f positive, convex f negative
worked — concave mirror
p = 30 cm, f = 10 cm.
1/q = 1/10 − 1/30 = 2/30 → q = 15 cm · m = 15/30 = 0.5, real & inverted
Board practical: find f of a convex lens from f = pq/(p + q); e.g. p = 30.0 cm, q = 21.4 cm → f = 642/51.4 = 12.5 cm.
8 — Exam recap
- ∠i = ∠r from the normal; plane image virtual, q = p, laterally inverted; convex mirror → small, erect, wide view.
- f = R/2; 1/f = 1/p + 1/q; m = q/p — mirrors and lenses alike.
- n = sin i / sin r = c/v; apparent depth = real/n (pools look shallow, straws snap).
- TIR when denser→rarer and i > C, sin C = 1/n — fibres, diamonds, mirages, prisms.
- P = 1/f(m) dioptres; myopia → concave, hypermetropia → convex.
- Magnifier M = 1 + d/f; dispersion fans white light into a rainbow.