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A straw in a glass of water looks bent. Every ray optics chapter explains why with one equation, Snell's law. Yet the man it is named after never published it, and at least two others found it independently. This post covers who Willebrord Snell was, the tangled history of the law, worked examples for water and glass, the slips students make, and what you can take from his way of working.
Who was Willebrord Snell?
The MacTutor biography from the University of St Andrews gives his dates as 13 June 1580 to 30 October 1626, both in Leiden. He wrote in Latin as Willebrordus Snellius. His father, Rudolph Snell, was professor of mathematics at Leiden, and Willebrord studied privately with Ludolph van Ceulen. Travelling in 1600 and 1601 he met Tycho Brahe, helped with observations, and came to know Johannes Kepler. In 1613 he succeeded his father as professor.
His best-known book in his lifetime was Eratosthenes Batavus (1617), on measuring the Earth. MacTutor describes how he used a chain of triangles, starting from a baseline between his house and a church spire, to find the distance between the towns of Alkmaar and Bergen-op-Zoom, about 130 km apart. This method, triangulation, became the basis of surveying. In 1621 his Cyclometricus improved the old method of estimating π with polygons.
Who really discovered the law of refraction?
MacTutor's history of light, Light through the ages, sets out the sequence:
1601: Thomas Harriot in England found the sine law of refraction but did not publish it.
1621: Snell found the law independently, again without publishing.
1637: René Descartes published it in La Dioptrique, an appendix to his Discourse on Method.
The NCERT Class 12 Wave Optics chapter opens with that last step: "In 1637 Descartes gave the corpuscular model of light and derived Snell's law." Snell's version survives in a manuscript now in the University of Amsterdam library. The MacTutor biography quotes the historian Klaus Hentschel, whose 2001 study of the manuscript argues that Snell's trigonometry from surveying helped him, and that he found the law "in the secant form" rather than with sines. His result became widely known when Christiaan Huygens published it in his Dioptrica in 1703.
What does Snell's law say?
The NCERT Ray Optics chapter says "Snell experimentally obtained the following laws of refraction": the incident ray, the refracted ray and the normal lie in one plane, and sin i / sin r = n21, the refractive index of the second medium relative to the first. An equivalent form is n1 sin i = n2 sin r. If light enters a denser medium (n21 > 1), it bends towards the normal.
Going the other way, from denser to rarer, the refracted angle reaches 90° at the critical angle, where sin ic = 1/n. NCERT's Table 9.1 lists 48.75° for water (n = 1.33) and 41.14° for crown glass (n = 1.52). Beyond that angle there is no refracted ray: total internal reflection, the principle of optical fibres.
Worked examples: water and glass
Example 1: air into water. A ray in air meets water (n = 1.33) at i = 45°. Find r.
n1 sin i = n2 sin r, so sin r = (1.00 × sin 45°) ÷ 1.33.
sin 45° = 0.7071, so sin r = 0.7071 ÷ 1.33 = 0.532.
r = 32.1°. The ray bends towards the normal, as expected.
Example 2: glass into air. A ray inside crown glass (n = 1.52) meets the surface at 30°. Find the angle in air.
sin r = 1.52 × sin 30° = 1.52 × 0.5 = 0.760.
r = 49.5°. The ray bends away from the normal.
Example 3: past the critical angle. Now the ray inside the glass meets the surface at 45°. Then 1.52 × sin 45° = 1.075, which is more than 1. No angle has a sine above 1, so there is no refracted ray. Check: 45° is larger than the critical angle of 41.1°, so the light is totally internally reflected.
What mistakes do students make with Snell's law?
Measuring from the surface. Both angles are measured from the normal. If a question gives the angle with the surface, subtract it from 90° first.
Swapping the indices. Write n1 sin i = n2 sin r with n1 on the side the light comes from. Ask: should the ray bend towards or away from the normal? Check your answer agrees.
Dividing the angles. The law is about sines, not angles. For small angles the ratio of angles comes close, which is why the error is easy to miss.
Forgetting the sine limit. If your sin r comes out above 1, the answer is total internal reflection, not an error in the question.
The JEE (Main) 2026 syllabus lists refraction at plane and spherical surfaces and total internal reflection, and also asks you to derive the laws of refraction with Huygens' principle. Check the current year's syllabus. Our post on common ray optics mistakes has more practice.
What can a student take from how Snell worked?
Carry tools across subjects. His trigonometry from surveying fed into optics.
Measure carefully. His triangulation, MacTutor notes, gave a good value for the Earth's size.
Publish your work. His law lay in a manuscript for decades while others printed theirs.
Read widely. Hentschel found that Snell's notes engage closely with earlier writers on optics, including Ibn al-Haytham.
A practice routine: solve the three examples again for diamond (n = 2.42), find its critical angle and compare with NCERT's 24.41°; then draw each ray with the normal marked. If bending towards or away from the normal still feels like guesswork, the Fermi Simulation Lab has interactive simulations for ideas that are easier to see than read.
Next step: shine a torch into a glass of water at different angles and sketch where the beam bends.
