What is refraction?
When light travels from one transparent medium into another, its speed changes. This change of speed makes the ray bend at the boundary. This bending is called refraction. When light passes from a less dense medium (such as air) into a denser medium (such as glass or water), it slows down and bends towards the normal. When it passes from a denser medium into a less dense medium, it speeds up and bends away from the normal. A ray that hits the surface along the normal (angle of incidence = 0°) is not bent.
The refractive index (n) of a medium measures how strongly it bends light. A higher refractive index means light slows down more and bends more.
Snell's law and refractive index
Key formula / Key formula
n = sin i / sin r (Snell's law)
where i = angle of incidence, r = angle of refraction (both measured from the normal).
Also n = c / v = speed of light in vacuum ÷ speed in the medium, and n = real depth / apparent depth.
Typical values: air ≈ 1.00, water ≈ 1.33, glass ≈ 1.50, diamond ≈ 2.42. Refractive index has no unit.
Worked example / Worked example
A ray of light enters glass (n = 1.50) from air at an angle of incidence of 30°. Find the angle of refraction.
n = sin i / sin r → sin r = sin i / n = sin 30° / 1.50 = 0.500 / 1.50 = 0.333.
r = sin⁻¹(0.333) = 19.5°. The ray bends towards the normal, as expected when entering a denser medium.
Worked example / Worked example
A coin lies at the bottom of a pool of water (n = 1.33) of real depth 8.0 cm. Find the apparent depth.
n = real depth / apparent depth → apparent depth = 8.0 / 1.33 = 6.0 cm. This is why a pool looks shallower than it really is.
Remember / Remember
- Denser medium → light slows down → bends towards the normal.
- Frequency does not change during refraction; speed and wavelength do.
- n = sin i / sin r only when light goes from air (vacuum) into the medium.