3.2c Lenses

The human eye is an amazing thing. We can identify differences in the position and colour of objects to an amazing degree of precision. But how does it do this? How are we able to count people in a crowd over 1 km away?
There are two key parts that make the eye work: The light sensitive cells at the back of the eye (the 'retina'), and the lens that focuses the light correctly. In this section, we will learn how lenses work, and how they are used in cameras, telescopes and other devices.

Figure 1: The human eye

Converging lenses

A lens is basically a curved piece of transparent material like glass. There are many different designs, but in this double award course we will cover converging lenses. Any lens rely on the principle that different parts of the lens refract light in different directions. A converging lens has a standard symbol as shown here:

Figure 2: A converging lens

Figure 4 below shows how a converging lens refracts light. Notice how the light is bent towards a single point, called the principal focus (also called the focal point). The distance from the centre of the lens to this principal focus is called the focal length of the lens. A thin lens will have a long focal length, and a thick lens a short focal length.

The principal axis is a line that passes through the centre of the lens at 90° to the glass.

Figure 4. A converging lens refracting light

When an object is a long way away from the lens, the light rays heading towards the lens are effectively parallel and will be refracted to the principal focus. This kind of diagram is called a ray diagram. It can be used to show how light from any object is refracted by a lens.

Ray Diagrams

Ray diagrams follow some very specific rules. If you follow the rules, you can work our where an image will be formed, and what this image will look like. Here is an example for you:

Figure 5. A converging lens ray diagram

There are several key features in the diagram above that you will need to learn.

1. To construct the diagram, just two lines are needed:

• a). A line from the top of the object and then through the middle of the lens. Any ray of light passing through the centre of the lens is not refracted, and so carries on in a straight line.
• b). A line from the top of the object that runs parallel to the centre line. This will be refracted and pass through the principal focus as shown in figure 4 and 5 above.

2. The point where the lines meet shows the where an image of the object will be produced. An image is a replica of the object seen by the eye. In this case we call it a real image because the image can be projected onto a screen. It is formed by real light rays converging at a point.

3. Notice that as well as being upside down (inverted), in this example the image is larger than the original object. It has been magnified. Images can be magnified (enlarged), diminished (made smaller) or stay the same size as the original object. This depends on the focal length and the placement of the object.

Questions:

1. Using information from the diagram shown in figure 5, state two features of the image shown.

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2. A converging lens is used form an image of a small pencil. The principal focus F of the lens is shown in the diagram:

• a) Complete an accurate ray diagram to show the image formed by this lens.
  (You could print out this diagram and then work on paper to complete it).
• b) State if the image is a the right way up or inverted.
• c) Comment on the relative size of the image compared to the original object.

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Virtual images

If an object is held close to a converging lens (closer than the principal focus) then a 'virtual' image is formed.

Figure 6. A converging lens ray diagram showing a virtual image

This is how this works:

Firstly we follow the 2 rules for drawing light rays, one going straight through the centre of the lens, and one going parallel to the centre line then through the principal focus. Once this is done, we can see that the light rays are moving apart (or 'diverging'). If the rays pass into our eyes, we are convinced that the rays came from a single point. We can draw some straight construction lines backwards to the left to find out where are brain tells us the top of the arrow was, or 'where the light rays came from'.

In this way, we can find out where we see an image of the arrow shown. Note that there are no real light rays coming from the image, it just appears to be there, so it is called a virtual image. A virtual image cannot be projected onto a screen as there are no actual light rays; it is like an optical illusion tricking the brain into seeing the object in a different place.

Notice that in this case, the image is magnified and upright. This is how a magnifying glass works, and it is why we hold the object close the the lens to magnify it effectively. It needs to be closer to the lens than the focal length.

Figure 7: A magnifying glass with a virtual magnified image
Niabot | CC BY-SA 3.0

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