Light
Shadows and straight-line light, mirrors, refraction and total internal reflection, lenses and the eye, colour and prisms, and the long effort to measure how fast light goes. The wave lab traces rays through glass, water and lenses with Snell’s law and the thin lens equation.
About this course
In 1849 Hippolyte Fizeau timed light over a round trip of about 17 km with a spinning wheel of 720 teeth. That is how the long effort to measure the speed of light appears in this course, as the last of six units on how light behaves. The earlier units are about what you can see with your own eyes: shadows, mirrors, glass, water, lenses and rainbows.
The units start with shadows. In a total solar eclipse the dark centre of the Moon's shadow often covers a strip less than 50 miles wide, while the partial shadow spans a thousand miles or more. Reflection follows, with the fact that a flat mirror only needs to be half your height to show your whole body. In the refraction unit, light inside a diamond can only get out if it meets the surface within 24.4° of the normal, which is why diamonds sparkle. Lenses and the eye show that the eye raises its power from about 50 to 54 diopters to focus on a book 25 cm away. In the colour unit, crown glass has an index of refraction of 1.530 for violet light at 410 nm and 1.512 for red at 660 nm, so violet bends more. The wave lab traces rays with Snell's law and the thin lens equation. Shrink the lamp to a point and the penumbra vanishes, and drag the object arrow past 2F to see the image shrink.
Dispersion is not always welcome. OpenStax points out that white light sent along an optical fibre would spread out in time, which is one reason fibre networks use lasers.
Before you start
Refraction and colour make more sense if you have met wavelength in Waves and sound, though the ray units on shadows and mirrors stand on their own. A few questions use sines and the lens formula, so Trigonometry is useful background, along with a calculator.
When you finish
Afterwards you can work out the width of a shadow with similar triangles, explain why a full-length mirror only needs to be half your height, and find the critical angle for diamond. You can locate the image formed by a lens, express the eye's power in diopters, say where the Sun must be for a rainbow, and follow Fizeau's toothed-wheel measurement of the speed of light.
- 1Light travels in straight lines: shadowsIn a total solar eclipse the dark centre of the Moon’s shadow often covers a strip less than 50 miles wide, while the partial shadow spans a thousand miles or more.
- 2Reflection and mirrorsTo see your whole body in a flat mirror you need a mirror only half as tall as you are, wherever you stand.
- 3Refraction and total internal reflectionLight inside a diamond can only get out if it meets the surface within 24.4° of the normal, which is why diamonds sparkle.
- 4Lenses and the eyeYour eye focuses on a book 25 cm away by raising its power from about 50 to 54 diopters, an 8% change.
- 5Colour, prisms and rainbowsCrown glass bends violet light at 410 nm a little more than red light at 660 nm, because its index of refraction is 1.530 for violet and 1.512 for red.
- 6Measuring the speed of lightIn 1849 Hippolyte Fizeau timed light over a round trip of about 17 km with a spinning wheel of 720 teeth.
Sources for this course (16)
- OpenStax College Physics 2e (openstax.org/books/college-physics-2e): 25.2 The Law of Reflection (θr = θi, diffuse vs mirror reflection, image as far behind the mirror)
- 25.3 The Law of Refraction (Roemer 1676 data -> 2.26 × 10⁸ m/s, about 25% low; Michelson rotating mirrors with a fixed mirror 35 km away, 0.04%; c = 2.99792458 × 10⁸ m/s; n = c/v; Table 25.1 air 1.000293, water 1.333, ice 1.309, crown glass 1.52, flint 1.66, polystyrene 1.49, zircon 1.923, diamond 2.419; Snell's law; 30.0° -> 22.0° gives 1.33; air to diamond 30.0° -> 11.9°; zircon 1.56 × 10⁸ m/s; Ibn Sahl 984; Snell 1580 to 1626; lawn-mower analogy)
- 25.4 Total Internal Reflection (mirror more than 90%; θc = sin⁻¹(n2/n1); polystyrene 42.2°, water 48.6°, diamond 24.4°; fibre optics, cladding; corner reflectors on bicycles and on the Moon; binoculars)
- 25.5 Dispersion (Kamal al-Din al-Farisi 1267 to 1319, camera obscura and a water-filled glass vessel; Theodoric of Freiberg; Ibn al-Haytham; about six rainbow colours; Table 25.2 n at 660/610/580/550/470/410 nm; violet bent most; rainbow seen looking away from the Sun; secondary rainbow from two reflections; lasers disperse little)
- 25.6 Image Formation by Lenses (ray tracing rules, P = 1/f in diopters, 1/do + 1/di = 1/f, m = −di/do, 0.750 m object and f = 0.500 m -> 1.50 m and m = −2.00, magnifier do 7.50 cm -> di −30.0 cm and m = 4.00, Table 25.3 three cases)
- 26.1 Physics of the Eye (cornea and lens act as one thin lens, most bending at the cornea, cornea n 1.38, lens-to-retina 2.00 cm, near point 25 cm, power 50.0 D to 54.0 D, hair 1.20 × 10⁻² cm at 60.0 cm)
- 27.3 (Young 1801)
- NASA science.nasa.gov/eclipses/geometry (umbra, penumbra; typical umbral path may be less than 50 miles wide, penumbra a thousand miles or more) and nasa.gov image article Diagram of Umbra and Penumbra (umbra shrinks, penumbra grows away from the Sun)
- NASA Visible Light page (Newton 1665 prism experiment, 380 to 700 nm)
- Royal Society, Fara 2015 commentary on Newton (1672) New Theory about Light and Colours (royalsocietypublishing.org/rsta/article/373/2039/20140213)
- NIST Meter page (Evenson group 299 792 456.2 ± 1.1 m/s; 1983 definition fixes c = 299 792 458 m/s) and NIST J. Res. 1972 measurement (tf.nist.gov/general/pdf/527.pdf)
- APS News July 2010, Fizeau (Galileo lanterns; Roemer 1676; Fizeau 1849, 313 300 km/s, about 5% high)
- Wikipedia Fizeau's measurement (8633 m, 720 notches, 25.2 turns per second -> 313 274 304 m/s, 4.5% high) and Speed of light (Galileo proposal 1638; Foucault 1862 298 000 ± 500 km/s, −0.60%; Michelson 1926 299 796 ± 4 km/s)
- Baez and DESY "How is the speed of light measured?" (same table)
- NASA Moon Fact Sheet (mean distance 384 400 km)
- IAU 2012 astronomical unit 149 597 870 700 m.
Checked: 2026-10-17