Refraction, Snell's law and dispersion of light
Light bends at the boundary of two media because its speed changes: sin i / sin r = μ₂/μ₁. A prism splits white light into seven colours.
Refraction of light
Refraction is the bending of light when it passes from one transparent medium to another. It happens because light travels at different speeds in different media. Light going from a rarer medium (such as air) into a denser medium (such as glass or water) slows down. So it bends towards the normal. Going from denser to rarer, it speeds up and bends away from the normal. The normal is an imaginary line at 90° to the surface. A straw in a glass of water looks bent because of refraction.
Laws of refraction and refractive index
- First law: the incident ray, the refracted ray and the normal at the point of incidence all lie in the same plane.
- Second law (Snell's law): sin i / sin r = μ₂ / μ₁. Here i is the angle of incidence and r the angle of refraction. μ₁ and μ₂ are the refractive indices of the first and second media.
- Refractive index (μ) of a medium = speed of light in vacuum ÷ speed of light in the medium: μ = c/v. It is a ratio, so it has no unit.
- A larger μ means light travels slower in that medium and bends more. Typical values: air about 1.0, water 1.33, glass about 1.5, diamond 2.42.
Using Snell's law
Light enters a transparent medium of refractive index √2 (about 1.414) from air (μ = 1) at an angle of incidence of 45°. Find (i) the angle of refraction (ii) the speed of light in the medium. (c = 3 × 10⁸ m s⁻¹)
- Given: μ₁ = 1, μ₂ = √2, i = 45°, c = 3 × 10⁸ m s⁻¹.
- (i) Snell's law: sin i / sin r = μ₂/μ₁, so sin r = sin i × μ₁/μ₂.
- sin r = sin 45° × 1/√2 = (1/√2) × (1/√2) = 1/2.
- sin r = 1/2, so r = 30°.
- (ii) μ = c/v, so v = c/μ = 3 × 10⁸ ÷ 1.414 ≈ 2.12 × 10⁸ m s⁻¹.
The angle of refraction is 30°, smaller than 45°, so the light bends towards the normal. Light travels at about 2.12 × 10⁸ m s⁻¹ in the medium (rounded to 3 significant figures).
Dispersion of light
Dispersion is the splitting of white light into its seven colours when it passes through a prism. The band of colours is called the spectrum: VIBGYOR (violet, indigo, blue, green, yellow, orange, red). It happens because the refractive index of glass is different for each colour. Each colour has a different wavelength (the length of one wave). Violet has the shortest wavelength and bends the most. Red has the longest wavelength and bends the least. A rainbow forms when tiny raindrops disperse sunlight.
How to draw dispersion by a prism
- 1Draw a triangle for the glass prism, with its base at the bottom. Label it glass prism.
- 2Draw a ray of white light striking the left face of the prism at an angle.
- 3Inside the prism, draw the ray bending towards the base.
- 4From the right face, draw a fan of seven rays spreading out towards a screen.
- 5Label the top ray red (least bent) and the bottom ray violet (most bent). Label the band on the screen spectrum (VIBGYOR).
A coin in a bucket of water looks raised, and a straw in a glass of lime juice looks bent, because of refraction. The rainbow after a monsoon shower is sunlight dispersed by raindrops.
2 marks: “State Snell's law of refraction.” The ratio of the sine of the angle of incidence to the sine of the angle of refraction equals the ratio of the refractive indices of the two media: sin i / sin r = μ₂/μ₁.
2 marks: “What is dispersion of light? Which colour deviates the most?” Splitting of white light into its seven colours by a prism; violet deviates the most and red the least.
4 marks: “State the laws of refraction. The speed of light in water is 2.25 × 10⁸ m s⁻¹. Find the refractive index of water.” Two laws; μ = c/v = (3 × 10⁸) ÷ (2.25 × 10⁸) = 1.33.
Fast to slow, bend towards; slow to fast, bend away. For the prism: Red Rests, Violet Veers (red bends least, violet most).