5.3 Lenses and ray diagrams — Practise with help

Work each problem first. Open a hint only if you are stuck, and the full working only to check.

Warm-up: remember

Answer these from memory. They use ideas from Sections 5.1 and 5.2.

Work out $\dfrac{40}{8.0}$ .
Convert 0.25 m to centimetres.
Which group of the spectrum has the higher frequency, red light or violet light?

Answers

$5.0$ .
$25\,\text{cm}$ .
Violet light.

If question 1 went wrong, remember that a ratio has no unit. If question 2 went wrong, remember that there are 100 cm in 1 m.

Practise with help

1. A magnifying glass forms an image 20 mm tall of an object 5.0 mm tall. Calculate the magnification.

Hint

Magnification is image height divided by object height. Both heights are already in millimetres, so the units match.

Next step

Write magnification $= \dfrac{20\,\text{mm}}{5.0\,\text{mm}}$ .

Full working

\begin{aligned} \text{magnification} &= \frac{20\,\text{mm}}{5.0\,\text{mm}} \\ &= 4.0 \end{aligned}

2. A lens has a magnification of 6.0. A bee in front of it is 1.5 mm long. Calculate the length of the image of the bee.

Hint

Rearrange the magnification relationship so that the image height is on its own.

Next step

Write image height $= \text{magnification} \times \text{object height}$ , then put in $6.0$ and $1.5\,\text{mm}$ .

Full working

\begin{aligned} \text{image height} &= 6.0 \times 1.5\,\text{mm} \\ &= 9.0\,\text{mm} \end{aligned}

3. A slide 5.0 cm tall is projected so that its image is 0.40 m tall. Calculate the magnification. Take care with the units.

Hint

Change the image height to centimetres before you divide. Make sure both heights are in the same unit.

Next step

$0.40\,\text{m} = 40\,\text{cm}$ . Now divide the image height by the object height.

Full working

\begin{aligned} \text{magnification} &= \frac{40\,\text{cm}}{5.0\,\text{cm}} \\ &= 8.0 \end{aligned}

4. Describe the two ray rules you use to draw a ray diagram for a convex lens.

Hint

One rule is about a ray that starts parallel to the principal axis. The other is about a ray that passes through the middle of the lens.

Next step

For the first rule, say which point the ray passes through after the lens. For the second rule, say whether the ray bends.

Full working

Rule 1: a ray that travels parallel to the principal axis is refracted through the principal focus on the other side of the lens.

Rule 2: a ray that passes through the centre of the lens continues in a straight line and does not bend.

The two rays meet at the top of the image.

5. A student looks at a small insect through a magnifying glass. The insect looks larger and the right way up. Explain whether this image is real or virtual.

Hint

A real image is inverted and can be put on a screen. Think about what the student actually sees.

Next step

Name the two properties of the image that the question gives you, and match them to the properties of a real or a virtual image.

Full working

The image is virtual. It is upright, not inverted, and it cannot be put on a screen. A virtual image forms where the rays only appear to come from, on the same side of the lens as the object.

This answer is a model answer for you to compare with your own wording.