Monday, April 12, 2010

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.

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