How Light Bends

What this book is about

Spectacles, a camera, a mirage, the rainbow, the internet arriving along the sea floor — there is one event behind all of it. Light entering one material from another changes speed, and changing speed changes direction.

Textbooks teach refraction with Snell's law — sin i over sin r is a constant, memorise it. What that constant is *of*, and why light bends at all, usually go unanswered. Here the answer comes first. Light travels more slowly in water; when one side of a ray slows before the other, the whole ray swings round — exactly as a car turns when one wheel drops into sand. Everything else in the book is a consequence of that one sentence.

You need to be able to divide, to know what an angle is and how to measure one with a protractor. Sine helps, and what little is needed is recalled here from volume 17.

Stop at page 26. The refractive index of water is worked out there by two entirely separate methods — once by measuring angles with a protractor, once by measuring depth with nothing but a ruler. Both give 1.33. That page is the spine of the book. Keep a bowl, a little water and a coin beside you; the experiment on page 74 takes ten minutes and makes the whole book stick.

What is inside

• Light bends: the stick that looks broken in a pond, why spearing a fish needs an aim

correction, the two angles and their names, and Snell's rule

• The refractive index — what the number actually means, how much in which medium, the coin

under water, two roads to one answer, and total internal reflection

• Lenses: prisms joined together, convex and concave, why three rays are enough, and the

lens equation

• The eye and spectacles — the eye as a camera, short sight, long sight and the ageing

lens, and what the number on a prescription means

• Nature's own tricks: mirage, white light split apart, the rainbow, seeing the sun after

it has set, and the internet through a thread of glass

• Who worked it out — Ibn al-Haytham, who found the law, Newton's second prism, whether

light is a wave, measuring its speed, and the glass we make today

• Two experiments, every formula on one sheet, worked exercises, a bilingual glossary and a quiz