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Reflection and Refraction of Light
Waves & Optics
Reflection is light bouncing off a surface, and refraction is light bending as it passes from one material into another. Together they explain mirrors, lenses, rainbows and mirages.
Reflection
Reflection happens when light strikes a surface and bounces back into the same medium. The law of reflection states that the angle of incidence equals the angle of reflection, with both angles measured from the normal. A smooth surface gives a clear, regular reflection, like a mirror, because all the rays reflect in the same direction. A rough surface scatters light in many directions, which is diffuse reflection, and is why a sheet of paper looks the same from any angle even though it reflects light. The image in a plane mirror is the same size as the object, upright, laterally inverted, and as far behind the mirror as the object is in front.
Refraction and Snell's law
Refraction is the bending of light as it crosses into a material where its speed is different. Light travels at 3.0 x 10^8 m/s in a vacuum, slower in air, slower still in water, and slower again in glass. The refractive index of a material is the ratio of the speed of light in a vacuum to its speed in that material. Snell's law relates the angles and refractive indices on the two sides of a boundary. When light enters a denser medium it bends toward the normal; when it enters a less dense medium it bends away. If it enters along the normal it does not bend at all.
Where you see it
A straw in a glass of water looks bent at the surface because light from the submerged part refracts as it leaves the water. A swimming pool looks shallower than it is for the same reason. Total internal reflection, when light in a dense medium hits the boundary at more than the critical angle and reflects entirely, is used in optical fibres to carry signals over long distances and in diamond cutting to make gems sparkle. Rainbows form when sunlight refracts into raindrops, reflects inside them, and refracts out again, splitting into colours because different wavelengths refract by different amounts.
📝 Worked example: light entering water
A ray in air hits water at an angle of incidence of 30 degrees. Refractive index of air n1 = 1.00, of water n2 = 1.33. Use Snell's law: n1 sin(theta1) = n2 sin(theta2). Substitute: 1.00 x sin(30 degrees) = 1.33 x sin(theta2). sin(30 degrees) = 0.50, so sin(theta2) = 0.50 / 1.33 = 0.376. theta2 = sin^-1(0.376) = 22.1 degrees. The ray bends toward the normal, from 30 degrees to about 22 degrees.
Common mistakes
- Measuring angles from the surface: angles of incidence, reflection and refraction are all measured from the normal, the line at right angles to the surface.
- Saying light always bends away from the normal entering a denser medium: it bends toward the normal when it slows down.
- Forgetting that reflection still happens at a refracting surface: some light is reflected and some refracted at every boundary.
Practice questions
- Light enters glass (n = 1.50) from air at 45 degrees. What is the angle of refraction?
Show answer
theta2 = sin^-1(sin 45 / 1.50) = sin^-1(0.707/1.50) = sin^-1(0.471) = 28.1 degrees.
- What is the critical angle for water to air (n_water = 1.33)?
Show answer
sin(theta_c) = 1.00/1.33 = 0.752, so theta_c = 48.8 degrees.
- A ray hits a plane mirror at 30 degrees to the normal. What is the angle of reflection?
Show answer
The angle of reflection is also 30 degrees, by the law of reflection.
Frequently asked questions
Why does light bend when it enters water?
It bends because light travels slower in the denser medium, so the wavefront changes direction at the boundary, unless it enters straight on.
Does total internal reflection happen in both directions?
No. Total internal reflection only happens when light travels from a denser medium to a less dense one at an angle above the critical angle.