Light: Reflection and Refraction

Light lets us see the world, and it behaves in beautifully regular ways. When it strikes a surface it reflects; when it passes from one material into another it bends, or refracts. From these two simple behaviours come mirrors, lenses, spectacles, cameras and microscopes. Understanding reflection and refraction is the heart of the physics of light.

Reflection is the bouncing back of light from a surface. It follows two simple laws of reflection:

• The angle of incidence equals the angle of reflection (the angles the incoming and outgoing rays make with the normal, a line at right angles to the surface).
• The incident ray, the reflected ray and the normal all lie in the same plane.

A smooth surface like a mirror gives a clear image, whereas a rough surface scatters light in all directions.

Curved mirrors form images in useful ways:

• A concave mirror curves inward and converges light to a focus. Depending on where the object is placed, it can form a real, inverted image or a magnified, upright one. It is used in shaving mirrors, torches and headlights.
• A convex mirror curves outward and diverges light. It always forms a small, upright image and gives a wide field of view, which is why it is used as a vehicle rear-view mirror.

Refraction is the bending of light as it passes from one transparent medium into another (say, from air into water). It happens because light travels at different speeds in different materials.

• Going into a denser medium (like glass), light slows down and bends towards the normal.
• Going into a rarer medium, it speeds up and bends away from the normal.

How much a medium bends light is given by its refractive index. Refraction explains why a pencil looks bent in a glass of water and why a pool looks shallower than it is.

The atmosphere itself bends light. Air is made of layers of varying density, and starlight refracts a little as it passes through each layer. The layers keep shifting, so the bending keeps changing. This makes the apparent position and brightness of a star flicker. That is why stars twinkle. Planets do not twinkle: they are much closer, so they appear as small discs rather than points, and the flickers from different parts of the disc cancel out.

Atmospheric refraction creates other optical illusions:

• Early sunrise and late sunset: the atmosphere bends sunlight around the curve of the Earth. We see the sun about two minutes before it actually rises and for about two minutes after it actually sets.
• The sun at the horizon: at sunrise and at dusk the sun looks larger, flattened or distorted. This apparent change in size and shape is an optical illusion caused by refraction in the atmosphere, not a real change in the sun.

The red colour of the rising and setting sun, by contrast, is caused by scattering, not refraction. Keep the two effects separate: refraction shifts and distorts, scattering colours.

When light tries to pass from a denser medium into a rarer one at a large enough angle, it cannot escape. The surface acts like a perfect mirror and the light bounces back inside the denser medium. This is total internal reflection.

The rainbow depends on it. A rainbow forms by three phenomena acting together inside each raindrop:

• Refraction: sunlight bends as it enters the drop.
• Dispersion: the drop splits the light into its colours, like a tiny prism.
• Total internal reflection: the coloured light reflects off the back of the drop, then refracts again as it leaves.

So a rainbow is not dispersion alone. Refraction, dispersion and total internal reflection are all involved.

A lens is a piece of transparent material that refracts light to form images:

• A convex (converging) lens is thicker in the middle and brings light rays together. It can form magnified images and is used in magnifying glasses, cameras and to correct long-sight.
• A concave (diverging) lens is thinner in the middle and spreads light out. It forms small, upright images and is used to correct short-sight.

The power of a lens to bend light is measured in dioptres. Lenses are the basis of spectacles, microscopes and telescopes.

The human eye is a living application of the lens. It works much like a camera. Light enters through the cornea and the pupil, passes through the lens, and is focused onto the retina at the back of the eye, where it forms an image. The retina sends signals along the optic nerve to the brain.

A special feature is accommodation: the eye's lens can change its shape, becoming thicker or thinner. This lets the eye focus on objects both near and far. It is done by the ciliary muscles. The iris controls the size of the pupil, adjusting how much light enters.

Sometimes the eye cannot focus properly, causing defects of vision that are corrected with lenses:

• Myopia (short-sightedness): distant objects look blurred because the image forms in front of the retina. Corrected with a concave lens.
• Hypermetropia (long-sightedness): nearby objects look blurred because the image forms behind the retina. Corrected with a convex lens.
• Presbyopia: with age, the eye loses the power of accommodation, often needing bifocal lenses.

Spectacles, contact lenses and surgery restore clear vision.

White light is not a single colour but a mixture. When white light passes through a prism, it splits into a band of seven colours: violet, indigo, blue, green, yellow, orange and red. This splitting is called dispersion, and the band of colours is the spectrum.

Dispersion happens because each colour bends by a slightly different amount. Raindrops act as tiny prisms and disperse sunlight, which is one step in making the rainbow after rain. As explained above, the full rainbow also needs refraction into the drop and total internal reflection at its back.

When sunlight passes through the atmosphere, it is scattered by the tiny molecules and particles of air. Blue light, having a shorter wavelength, is scattered much more than red.

This scattering of light explains two everyday sights:

• the sky looks blue, because scattered blue light reaches our eyes from all directions, and
• the rising and setting sun looks red, because near the horizon sunlight travels through more air. Most of the blue is scattered away, leaving the red to reach us.

Different light sources give out light with very different colour content. The range of colours a source emits is called its spectrum. A source that emits essentially a single colour, and so a single wavelength, is called monochromatic. A source that mixes many wavelengths appears white or near-white and can render the true colours of objects.

Street lighting offers a clear comparison between two common sources:

• Sodium vapour lamp: an electric discharge through sodium vapour produces the familiar deep yellow glow of older street lights. Its visible light is almost monochromatic, so objects under it lose their natural colours. The glowing tube radiates in all directions, a full 360 degrees, so reflectors are needed to push the light downward and much of it is wasted as glare and sky glow.
• LED lamp: a light emitting diode is a semiconductor device that emits light when current passes through it. LEDs are naturally directional, sending light where it is aimed rather than all around. They can be tuned to give a broad spectrum, which means far better colour rendering on the street. They are also more energy efficient and have a much longer life span than sodium lamps, which is why cities are replacing sodium street lights with LEDs.

The key contrasts to remember: sodium light is omnidirectional and nearly one colour, while LED light is directional, longer lasting and rich in colour.