Physics
Cambridge IGCSE

TOPIC 3: WAVES

# 6.6 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

## Lenses and refraction

A lens is basically a curved piece of transparent material like glass. There are many different designs, but here we will cover the two basic designs: thin converging and diverging lenses. Both of these lenses rely on the principle that different parts of the lens refract light in different directions. Each of the lenses has a standard symbol as shown here:

Figure 2: A converging lens

Figure 3: A diverging lens

## Converging lenses

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.

Any two from:

• Using the diagram, the image height is larger than the object so it has been magnified/enlarged.
• The rays of light meet at a point and could be projected on a screen, so the image is real (not virtual -see later discussion on virtual images).
• The image is further away from the lens than the object
• The image is upside down/inverted.

Remember if it asks for 2 features, only list 2!

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 real or virtual image.
• c) Comment on the relative size of the image compared to the original object.

a) The completed ray diagram should look like this:

Notice that one ray goes straight through the centre of the converging lens and is not refracted - it carries on in a straight path. Another ray runs parallel to the centre line, and then is refracted through the principal focus.
Where these two lines meet, the image of the pencil tip will be found.

b) The image is formed by real light rays and can be projected on to a screen, so it is a real image.

c) Using measurements from a print out, the image was found to be 2.8 cm compared to 6.2 cm for the object. The image has been diminished/reduced in size (by a factor of over 2, compared to the object)

### 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

Note that students taking the extended course with supplementary content should be able to draw the ray diagram shown in figure 6 to show how a virtual image is formed.

## Diverging lenses

Diverging lenses refract light rays in the opposite direction to converging lenses. This means that - instead of coming together at a point, they always diverge as shown in figure 8:

Figure 8. The principal focus of a diverging lens

In fact, they diverge as if the rays had all come from one point, as shown in the second diagram, and this is the principal focus of a diverging lens. For this reason, diverging lenses always produce virtual images. The next diagram shows how a virtual image is produced using a diverging lens:

Figure 9. A virtual image formed by a diverging lens

The rules for completing this ray diagram are very similar: One straight line passes from the top of the object and through the centre of the lens. Another is refracted, but this time instead of passing through the focus, it is bent so that it appears to come from the focus on the left side of the lens. This gives us our 2 rays, and we can now find where they appear to have come from. You do not need to be able to draw this diagram in the exams - just describe that the rays diverge, creating a virtual image when the lines are extrapolated backwards, on the same side of the lens as the object.

Questions:

3. Lenses can be used to produce real and virtual images. State the type of image(s) produced by:

• a) diverging lenses
• b) converging lenses

a) Diverging lenses always produce virtual images.

b) Converging lenses can produce both virtual and real images (depending where the object is placed).

4. Parallel light rays pass from a distant object pass through a diverging lens. Draw a ray diagram to show how they are refracted. Use the correct symbol for a diverging lens.

a) The completed ray diagram should look like this with the correct symbol for the lens, and diverging rays (spreading outwards):

## Wearing Glasses

Wearing glasses to correct problems with vision has had a profound effect on society, allowing people to continue to read, work and go about their daily lives without vision problems. Glasses can be worn for a wide variety of issues, but the most simple problems are when the eye focuses light in the wrong place for either distant or close objects.

In normal vision, the lens in the eye acts like the converging lens shown in question 2 above, with a real, diminished and inverted image being projected onto the back of the eye, where sensitive cells detect the light. it's interesting to think that our brains must be 'decoding' the inverted image, so that we see everything the right way up!

### Long-sightedness

This occurs when a person can focus clearly on distant objects. However when the object is close to the eye, the light rays are diverging as they travel into the eye. The eye lens in this case focuses the rays behind the back of the eye and everything looks blurred.

To fix long-sightedness, the light rays need to be refracted inwards, and this needs an additional converging lens, worn as glasses by the individual when reading, or looking at a computer screen or similar.

Figure 10 shows how the light rays are not in focus at the back of the eye when the object is nearby, and how this problem is fixed with a converging lens.

Notice that figure 10 and 12 give a hint as to the cause of the problem in some people, where the shape of the eye ball is too long or too short, and this leads to the problems with focusing correctly.

Long-sightedness is sometimes called far-sightedness.

Figure 10: Long-sightedness fixed by a converging lens

### Short-sightedness

As you may have guessed, this occurs when a person can focus clearly on nearby objects. However when the object is far away, the light rays are just about parallel. The eye lens in this case focuses the rays in front of the back of the eye and - again - everything at a distance looks blurred.

Figure 11. Short-sightedness with blurred background (Myopia)

Figure 12: Short-sightedness fixed by a diverging lens

To fix this, glasses with diverging lenses are required as shown in figure 12. The lens bends the light away from the principal axis, correcting the problem and allowing the rays to focus on the back of the eye correctly.

Short-sightedness is sometimes called near-sightedness or myopia.

Questions:

5. Choose the correct words/phrases from the box below to complete the passage shown here:

 near behind virtual diverging in front of distant converging real

A person with short-sightedness will find that _________ objects appear blurred. The image is ___________, but is being focused ________ the sensitive cells at the back of the eye. To correct this, a ________ lens is required.

A person with short-sightedness will find that DISTANT objects appear blurred. The image is REAL, but is being focused IN FRONT OF the sensitive cells at the back of the eye. To correct this, a DIVERGING lens is required.

Tier

## Please choose a tier of entry

 Extended Tier (Core and Supplementary content, Grades A* to G) Core Tier (Core content only, grades C to G) Remember my choice