Basic Optics: The principles of imaging - lenses and pinholes

We are all familiar with imaging - everything we see results from the imaging of the world on to our retina. Cameras image the world onto a film or a CCD, usually through a lens. Projectors display images on a screen, but how and why does imaging work.

If we imagine the light either bouncing, or being emitted from an object. That light passes through a hole, and then on to a screen. How do we know whether an image will form? For a large hole, like the one in the following picture, the light from any point on the object, on the right hand side ( I have chosen a picture of Darwin) may land on several points on the screen. As a result, the image will appear bright (because plenty light gets through the hole) but blurry (because the light from a point can hit a larger area on the screen.

The more we shrink the hole down, the more the light from the object is limited on the screen - however the less light gets through, so we have a much more sharply defined object, but it's also much darker.

Finally, if we introduce a lens into the larger hole, the light is bent so that (if the object and image are in the right places) all the light passing through the hole will land at the same point on the screen, and so we now have a bright object in good focus.

For a pinhole, it does not matter where the object and screen are, the image will always be in focus, however for a lens it does. There is a simple formula which tells us where the object and image are, depending on the focal length of the lens. The focal length is the distance at which an object at infinity is focussed. So for example when you hold a magnifying glass to focus the sun on to a point, it is the distance from the paper at which the spot is smallest and hottest. The formula that tells us where the object and image are is:

S1 and S2 are the object and image distances. It doesn't matter which way round, though the magnification will be affected by the different possible object and image distances.

This is a very simplified formula though, and depends on a number of considerations being true. The formula relies on what is known as the paraxial approximation - all the rays of light must be passing fairly close to the optical axis - a straight line passing out from the centre of the lens, perpendicular to the lens. if the rays pass close to the edge of the lens, or at a steep angle to the lens, then the image may be distorted, causing a number of optical aberrations (spherical aberrations, coma, field curvature). Also it ignores the different refractive indices of different wavelengths of light. In the same way as light is bent as it passes through a prism or a raindrop, and split up into different colours, the light of different colours passing through a lens may be focussed in different places. This is called chromatic aberration - and may often be seen towards the edges of lenses or pictures.

The Ancient History of Optics

People have puzzled and pondered over how we see for many thousands of years, though a more complete understanding of optics was not truly available to us until more recent centuries through the work of scientists like Newton, Young, Maxwell and Dirac. Some of the earliest known writings on optics date back to the Ancient Greeks. The majority of the earliest ideas on optics were largely speculation. In the fifth century BC for example, the greek philosopher Empedocles hypothesized that the eye contained fire, which shone out from the eye illuminating objects so that they could be seen. Of course this raises many questions, such as "why can't we see at night then" and "why don't objects appear incredibly bright when several people look at them" - for the former question Empedocles thought that there may be some interaction between the rays from the eyes, and rays from a source like the Sun or a candle. Unfortunately the concept of Occam's Razor (entia non sunt multiplicanda praeter necessitatem - or entities must not be multiplied beyond necessity) wasn't devised until the 14th century, or Empedocles' contemporaries may have suggested doing away with the eye-beams and just leaving the rays from bright objects like the Sun. Still, it was relatively early days, and there were many great thinkers to come, who would apply their minds to the problem of light and vision.

To backtrack a little here, while there was no theoretical understanding of light and optics, People had still made practical applications of optical components and light itself. One of the earliest known lenses for example was the Nimrud lens, shown here - a piece of shaped glass some 3000 years old in the remains of the ancient city of Nimrud, which lies within modern-day Iraq. This lens was discovered by Austen Henry Layard in the mid 19th century, and may have been used as a magnifying lens, either for looking at objects or starting fires. Many similar lenses exist through the ancient Greek, Roman, Babylonian and Egyptian cultures. These though tended to be carved from crystal or glass spheres filled with water.

Back on to the theory. A couple of hundred years after Empedocles speculated on how vision worked, Euclid wrote Optics, which was one of the first texts to study the geometrics of optical systems in more mathematical detail. Ptolemy, this time a Roman Citizen (though possibly of greek ancestry) who lived between the first and second centuries BC, extended this work futher. His writings are considered some of the most important writings on optics before Newton, although they survive only as translations into Arabic - the originals having been lost. In this, he introduces many of the important properties of optical systems, talking about light, refraction, reflection and colour (all things I will get on to later)

Not all of these early studies were limited to the Greek and Roman empires though, much important early work was also carried out by Arabic scholars such as Ibn Sahl (10th century BC) who discovered the law of refraction (now known as Snell's law) and Ibn Al-Haytham (10th-11th century BC) who did away with Empedocles' rays from the eyes and more carefully defined what the rays were.

Things lay relatively quiet on the optics front then, until the Rennaisance when scientists such as Johannes Kepler and Willebrord Snellius began investigating the mathematical and physical behaviour of light. That though, will have to wait until later.