5.3 Lenses and ray diagrams — Practise

Work through these on your own. For a calculation, write the relationship first and keep the units with your numbers. For an explanation, answer in full sentences.

Both the questions and the answers below come from a set that is checked by computer every time the book is built.

A lens forms an image 12 mm tall of an object 4.0 mm tall. Calculate the magnification.
A lens forms an image 30 mm across of a coin 6.0 mm across. Calculate the magnification.
A slide 4.0 cm tall is projected so that its image is 0.20 m tall. Calculate the magnification. Take care with the units.
A lens has a magnification of 4.0. An object 7.0 mm tall is placed in front of it. Calculate the height of the image.
A lens has a magnification of 5.0. The image of an insect is 45 mm long. Calculate the length of the insect.
The visitor centre lens projects a picture 2.0 cm tall so that its image is 0.30 m tall. Calculate the magnification.
A ray of light enters a convex lens parallel to the principal axis. Describe the path of the ray after it leaves the lens, and name the point it passes through.
Describe how to draw a ray diagram to find the image formed by a convex lens. Include what you must label.
Compare a real image with a virtual image. State one difference in how each is formed.
A convex lens and a concave lens are each held in sunlight. Describe the effect each lens has on a beam of parallel rays.
Explain why magnification has no unit.
A lens has a magnification of 2.5. An object is 1.2 cm tall. Say which form of the magnification relationship you will use, then calculate the height of the image.
A magnifying glass forms an image of a bee. The image is 27 mm long and the bee is 4.5 mm long. Calculate the magnification.

Answers and concise solutions

1. Magnification of the lens

Answer: magnification $= \dfrac{12\,\text{mm}}{4.0\,\text{mm}} = 3.0$ .

2. Magnification of the lens

Answer: magnification $= \dfrac{30\,\text{mm}}{6.0\,\text{mm}} = 5.0$ .

3. Magnification of the projected image

Answer: Convert 0.20 m to 20 cm. Then magnification $= \dfrac{20\,\text{cm}}{4.0\,\text{cm}} = 5.0$ . The ratio has no unit.

4. Height of the image

Answer: image height $= \text{magnification} \times \text{object height} = 4.0 \times 7.0 = 28\,\text{mm}$ .

5. Length of the insect

Answer: object height $= \dfrac{\text{image height}}{\text{magnification}} = \dfrac{45\,\text{mm}}{5.0} = 9.0\,\text{mm}$ .

6. Magnification of the projected picture

Answer: Convert 0.30 m to 30 cm. Then magnification $= \dfrac{30\,\text{cm}}{2.0\,\text{cm}} = 15$ .

7. The path of the ray

The ray bends and travels through the principal focus on the other side of the lens.
The point is the principal focus, where rays parallel to the principal axis meet.

8. How to draw the ray diagram

Draw the principal axis as a straight line through the centre of the lens.
Draw the convex lens as a vertical line across the axis and mark the principal focus on each side.
Draw one ray from the top of the object parallel to the axis, then through the principal focus.
Draw a second ray from the top of the object straight through the centre of the lens.
Where the two rays meet, draw the image and label it as inverted.

9. A comparison of real and virtual images

A real image forms where rays of light actually meet. It can be put on a screen and is inverted.
A virtual image forms where rays only appear to come from. It cannot be put on a screen. It is upright, and a magnifying glass makes one.

10. The effect of each lens

The convex lens brings the parallel rays together to a focus. It is a converging lens.
The concave lens spreads the parallel rays apart. It is a diverging lens.

11. Why magnification has no unit

Magnification is the image height divided by the object height.
Both heights are lengths in the same unit, so the units cancel and the answer is a plain number.

12. Height of the image

Answer: Use image height $= \text{magnification} \times \text{object height} = 2.5 \times 1.2 = 3.0\,\text{cm}$ .

13. Magnification of the lens

Answer: magnification $= \dfrac{27\,\text{mm}}{4.5\,\text{mm}} = 6.0$ .