Unit 3 · Lesson 3.6.3
Magnification
Calculate magnification from object and image heights, and decide whether an image is magnified, the same size or diminished.
The Magnification Equation
Magnification compares the size of the image with the size of the object.
Definition
- Magnification is the image height divided by the object height, so it tells how many times larger the image is than the object.
No units
- Magnification is a ratio with no units, so the object and image heights must be measured in the same unit before dividing.
Magnified
- A magnification greater than 1 means the image is larger than the object.
Diminished
- A magnification less than 1 means the image is smaller than the object, as happens for a distant object seen through a camera lens.
| Object height | Image height | Magnification | Image size |
|---|---|---|---|
| 4.0 cm | 10.0 cm | 2.5 | Magnified |
| 4.0 cm | 2.0 cm | 0.5 | Diminished |
| 4.0 cm | 4.0 cm | 1.0 | Same size |
Rearranging the Equation
1
Write the equation as magnification = image height ÷ object height, and substitute the known values with the same units.
2
To find an image height, multiply the magnification by the object height.
3
To find an object height, divide the image height by the magnification.
4
Check the answer by confirming that a magnification above 1 gives an image taller than the object.
Factors Affecting Magnification
Factors Affecting Magnification
Object distance
- Moving the object closer to a converging lens, within its focal length, increases the magnification of the image formed.
Lens power
- A stronger lens with a shorter focal length gives a greater magnification for the same object distance.
Measuring
- Measure both heights from the same scale drawing or photograph, using the same ruler units throughout.
Accuracy
- Measure the image height at its widest point, and check that the object height is measured at the same scale.
Worked Example
Question: A magnifying glass forms an image of a 4.0 cm long insect. The image is 10.0 cm long. Calculate the magnification and state whether the image is magnified.
- Step 1: Write magnification = image height ÷ object height.
- Step 2: Substitute the values with the same units: 10.0 cm ÷ 4.0 cm.
- Step 3: Calculate 10.0 ÷ 4.0 = 2.5, with no units.
Answer: The magnification is 2.5, so the image is magnified.
Exam Checklist & Tips
3.6.3 – Key Points for the Exam
- Magnification: The ratio of image height to object height, with no units.
- Image height: The height of the image, measured in the same unit as the object height.
- Object height: The height of the object being imaged, measured in the same unit as the image height.
- Magnified image: An image with a magnification greater than 1.
- Diminished image: An image with a magnification less than 1.
Common Mistakes
- Dividing the object height by the image height, which gives the reciprocal of the magnification.
- Using mixed units, such as centimetres for the image and millimetres for the object, without converting first.
- Giving magnification a unit such as cm, when it is a ratio with no units.
- Stating that a magnification of 0.5 means the image is magnified; it means the image is diminished.