Drawing on the two previous postings in this 'blog we are now able to create a basic model for image formation. This is not a thorough approach to image formation but it is enough to illustrate the operation of a simple lens.

The reason why we can see something is because light from the object reaches our eyes. Sadly, it is not enough for a sensor (in this case our eyes) simply to receive light from an object; the sensor must also process the light to construct a picture of the original object. This process is known as image formation.

Except in the case of luminous objects, the light that we see originates from a separate source and is simply reflected by the object. This can cause some odd effects when the source emits coloured light and the object is differently coloured, giving rise to either confusion or ambiguity in the colour that is seen.

It is usual for light to be reflected in all directions, meaning that the object can be seen from all angles. Unfortunately, this means that the sensor receives light from lots of different parts of the object at the same time and for a picture to be formed there needs to be a way of distributing the light across the image in the same pattern as it was reflected by the object. This is achieved using either a pinhole (discussed in an earlier blog entry) or a lens.

The crucial feature for image formation is a singular point that maps light from the object into the same pattern in the resulting picture: that point is the focus of the lens.

The diagram above shows how this work in practice by considering just two rays of light originating from the same point on the original object. These are not random rays but rather are one ray that travels parallel to the optical axis of the lens (the red line) and one that passes straight through the centre of the lens.

To get a better understanding image formation, let’s deal with the second ray first. This beam of light is straight because the lens is symmetrical and whatever happens to the ray in the left-hand side of the lens (above the optical axis) will be exactly the opposite of what happens in the right-hand side of the lens (below the optical axis). So even though the beam will be deflected at different points, the overall effect is for these deflections to cancel-out and leave the appearance of an undeflected ray.

The other ray, which travels parallel to the optical axis until it encounters the lens, will (by definition) be deflected to pass through the focus of the lens on the other side (as was explained in the previous instalment).

We have already seen that in order to compile the light beams into a meaningful picture it is necessary to create the same pattern on the image plane as exists on the object plane, and this means that every ray that left the same point on the object must meet at the same point in the image. Although there are only two rays shown above, the diagram clearly meets this criterion and therefore can be used to explain image formation.

This is not a proper proof of image formation so much as an illustrated explanation of the effect: it is simplified but it is essentially correct.

Astute readers might already have an inkling about how this same construction can be used to illustrate image defects – and that’s exactly what I’ll look at next time.