Light — Reflection and Refraction

Light is a form of energy that lets us see. Light travels in straight lines, and we see objects when light from them enters our eyes. When light travelling in one direction strikes a surface, it bounces back — this bouncing back of light from a surface is called reflection of light. Smooth, shiny surfaces such as mirrors reflect light very well, producing clear images. To describe reflection, we use a few terms: the incident ray is the ray of light striking the surface, the reflected ray is the ray that bounces back, and the normal is an imaginary line drawn perpendicular (at right angles) to the surface at the point where the ray strikes.

Reflection follows two simple laws of reflection. The first law states that the angle of incidence is equal to the angle of reflection — the angle the incident ray makes with the normal equals the angle the reflected ray makes with the normal. The second law states that the incident ray, the reflected ray, and the normal all lie in the same plane (they are coplanar). These two laws hold for reflection from any surface and let us predict exactly how light will bounce.

A plane mirror is a flat, smooth, reflecting surface (an ordinary mirror). When we look into a plane mirror, we see an image of ourselves. The image formed by a plane mirror has definite characteristics. It is virtual (it cannot be caught on a screen, as it only appears to be behind the mirror) and erect (the right way up). The image is the same size as the object, and it is as far behind the mirror as the object is in front — the image distance equals the object distance.

A plane mirror image also shows lateral inversion — its left and right appear interchanged. This is why the word "AMBULANCE" is written reversed on the front of ambulances, so that drivers ahead see it the right way round in their mirrors, and why your right hand appears as the left hand of your image. So the image in a plane mirror is virtual, erect, the same size as the object, at an equal distance behind the mirror, and laterally inverted. These properties of reflection and plane mirrors form the foundation for studying curved mirrors, refraction, and lenses.

Besides flat (plane) mirrors, there are curved mirrors, whose reflecting surface is curved like part of a sphere. There are two main kinds. A concave mirror is curved inward (its reflecting surface caves in, like the inside of a spoon's bowl). A convex mirror is curved outward (its reflecting surface bulges out, like the back of a spoon). These curved mirrors reflect light in special ways and form images very different from those of plane mirrors, making them useful for many purposes.

To describe curved mirrors, we use some standard terms. The pole (P) is the centre of the mirror's reflecting surface. The centre of curvature (C) is the centre of the sphere of which the mirror is a part. The principal axis is the straight line passing through the pole and the centre of curvature. The focus (F) is the point on the principal axis where rays of light parallel to the axis meet (for a concave mirror) or appear to come from (for a convex mirror) after reflection. The focal length (f) is the distance from the pole to the focus. These terms let us describe how each mirror forms images.

A concave mirror is a converging mirror: it brings parallel rays of light together at its focus. Because of this, a concave mirror can form different kinds of images depending on where the object is placed — the image may be real or virtual, magnified or diminished, erect or inverted. When the object is very close to a concave mirror, it forms a magnified, erect, virtual image; this is why concave mirrors are used as shaving and make-up mirrors and by dentists, and as the reflectors in torches, headlights, and searchlights (where a bulb at the focus sends out a parallel beam).

A convex mirror is a diverging mirror: it spreads parallel rays of light apart, so they appear to come from a focus behind the mirror. A convex mirror always forms a virtual, erect, and diminished (smaller) image, no matter where the object is. Because the image is smaller, a convex mirror shows a wide field of view — it lets us see a large area in a small mirror. This is why convex mirrors are used as rear-view mirrors in vehicles and as security mirrors in shops, giving the driver a wide view of the traffic behind. So concave and convex mirrors, with their converging and diverging actions, have many practical uses.

So far we have studied light bouncing off surfaces. But when light passes from one transparent medium into another — for example, from air into water or air into glass — something different happens: the light bends at the boundary between the two media. This bending of light as it passes from one transparent medium into another is called refraction of light. Refraction happens because light travels at different speeds in different media, and the change of speed at the boundary causes the ray to change direction.

Whether the light bends toward or away from the normal depends on the optical density of the media. A medium in which light travels more slowly is said to be optically denser. When light passes from a rarer medium to a denser medium (e.g. from air into glass or water), it slows down and bends toward the normal. When light passes from a denser medium to a rarer medium (e.g. from glass or water into air), it speeds up and bends away from the normal. If the light strikes the boundary straight on (along the normal), it passes straight through without bending.

The bending of light by refraction explains many familiar observations. A pencil placed in a glass of water looks bent or broken at the water's surface, because light from the submerged part bends as it leaves the water. A swimming pool looks shallower than it really is, because light from the bottom bends on leaving the water, making the bottom appear raised. A coin at the bottom of a vessel of water appears raised for the same reason, and stars appear to twinkle because of refraction of their light in the atmosphere.

The exact way light bends in refraction is described by Snell's law, which relates the angle of the incoming ray (angle of incidence) and the angle of the bent ray (angle of refraction) for a given pair of media — for any two media, the relationship between these angles is fixed. The key idea to remember is that refraction is the bending of light due to a change of speed when it crosses from one medium to another, bending toward the normal entering a denser medium and away from the normal entering a rarer one. Refraction is the basis for how lenses work, which we study next.

A lens is a piece of transparent material (usually glass) with at least one curved surface, which refracts (bends) light to form images. Lenses work by refraction, the bending of light we studied in the previous topic. There are two main types of lenses. A convex lens is thicker in the middle than at the edges; it is a converging lens, because it bends parallel rays of light to meet (converge) at a point called the focus. A concave lens is thinner in the middle than at the edges; it is a diverging lens, because it spreads parallel rays apart (diverges them), so they appear to come from a focus.

As with mirrors, lenses have an optical centre (the centre of the lens), a principal axis (the line through the optical centre), a focus (F), and a focal length (f) (the distance from the optical centre to the focus). A convex lens has a real focus where the rays actually meet, while a concave lens has a virtual focus from which the rays appear to spread.

A convex (converging) lens can form different kinds of images depending on the position of the object, much like a concave mirror. When the object is far away, a convex lens forms a real, inverted, diminished image (used in a camera and in our eye). When the object is very close (within the focal length), the convex lens forms a magnified, erect, virtual image — this is how a convex lens works as a magnifying glass (hand lens). A concave (diverging) lens, on the other hand, always forms a virtual, erect, diminished image, whatever the position of the object.

Lenses have many important uses. The convex lens is used in magnifying glasses, cameras, microscopes, and telescopes, and most importantly in the human eye, which contains a convex lens that focuses light onto the retina to form images. Convex lenses are also used in spectacles to correct certain vision defects, as are concave lenses. So lenses, by refracting light, allow us to magnify, focus, and form images — making them essential in optical instruments and in our own eyes, leading naturally to the study of the human eye.

Ordinary sunlight, or white light, appears colourless, but it is actually made up of seven colours mixed together. When white light passes through a prism (a triangular block of glass), it is split into a band of these colours. This splitting of white light into its component colours is called dispersion of light. Dispersion happens because the different colours of light bend by different amounts when they refract through the prism — red bends the least and violet the most.

The band of seven colours produced is called the spectrum, and the colours, in order, are red, orange, yellow, green, blue, indigo, and violet — easily remembered by the word VIBGYOR (read in reverse, from violet to red). These colours can also be recombined into white light, for example by passing them through a second, inverted prism, showing that white light truly is a mixture of all these colours. The most beautiful natural example of dispersion is the rainbow: tiny water droplets in the sky after rain act like prisms, dispersing sunlight into a spectrum across the sky.

The human eye is the organ that detects light and lets us see, and it works like a natural optical instrument. Light enters through the transparent front part, the cornea, passes through an opening called the pupil (whose size is controlled by the coloured iris), and then through the convex lens. The lens focuses the light onto the retina at the back of the eye, where a sharp, real image is formed; the retina sends signals along the optic nerve to the brain, which interprets them as the image we see. The eye lens can change its shape to focus on near and far objects — this ability is called accommodation.

Sometimes the eye cannot focus properly, leading to defects of vision that are corrected with spectacles (lenses). In myopia (short-sightedness), a person can see near objects clearly but not distant ones, because the image forms in front of the retina; it is corrected with a concave lens. In hyperopia (long-sightedness), a person can see distant objects but not near ones, because the image forms behind the retina; it is corrected with a convex lens. With age, the lens loses some flexibility, causing presbyopia, where focusing on near objects becomes hard. By understanding dispersion and the working and defects of the eye, we complete the study of light — from how it bends and forms colours to how we ourselves see the world.