Magnification by a mirror
How many times bigger or smaller the image is.
A shaving mirror
A shaving mirror shows your face larger than it is. A tiny mirror on a key ring shows it smaller. We would like one number that says how much bigger or smaller the image is.
How can we get that number?
What this lesson covers
The idea
Magnification m by a spherical mirror is the ratio of the image height h′ to the object height h, m = h′/h, and is also given by m = −v/u.
A shaving mirror
A shaving mirror shows your face larger than it is. A tiny mirror on a key ring shows it smaller. We would like one number that says how much bigger or smaller the image is.
How can we get that number?
- Divide the height of the image by the height of the object
- Subtract the height of the object from the height of the image
- Add the heights of the object and the image
Measure the image
Slide the object to C, and then to 30 cm. Compare the image height with the object height, and see two ways to get m.
Two ways, one number
At C the image was as tall as the object, so the ratio was 1. At 30 cm it was twice as tall, so the ratio was 2. The sign tells more about the image, and you meet it in the next lesson.
The magnification m produced by a spherical mirror is the ratio of the image height h′ to the object height h: m = h′/h. It is also given by m = −v/u.
Notes
Magnification m = h′/h, the ratio of image height to object height. For a mirror it is also m = −v/u.
Check yourself
What is the magnification of a spherical mirror?
An object is 4 cm tall. The mirror forms a virtual image 12 cm tall. What is the ratio h′/h?
Answer: 3
m = h′/h = 12 cm ÷ 4 cm = 3.
An object is at u = −30 cm and its image is at v = −60 cm. Use m = −v/u to find m.
Answer: -2
m = −v/u = −(−60 cm)/(−30 cm) = −2.
In m = −v/u, the image is taller than the object when
- The ratio of the image distance to the focal length. The ratio of image height to object height is the magnification. The image distance enters through m = −v/u, together with the object distance.
- The ratio of the height of the image to the height of the object — correct. Yes!
- The difference between the object height and the image height. Magnification is a ratio, found by dividing, not a difference found by subtracting.
- the image is nearer to the mirror than the object is. Then |v| is smaller than |u|, so the size of m is below 1 and the image is smaller than the object.
- the image is exactly as far as the object. Then |v| equals |u|, so the size of m is 1 and the image has the same size as the object.
- the image is farther from the mirror than the object is — correct. Yes!