Magnification by a lens
How many times bigger or smaller a lens makes the image.
A magnifying glass
A magnifying glass makes small print look bigger. A lens can also make the image smaller than the object. We want one number that tells how much.
How can we get that number?
What this lesson covers
The idea
Magnification produced by a lens 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 magnifying glass
A magnifying glass makes small print look bigger. A lens can also make the image smaller than the object. We want one number that tells how much.
How can we get that number?
- Divide the height of the image by the height of the object
- Subtract the object height from the image height
- Multiply the focal length by the object height
Measure the image
Slide the object to 15 cm, and then to 20 cm. Compare the image height with the object height, and see two ways to get m.
Two ways, one number
At 15 cm the image was twice as tall as the object, and upside down, so its height is negative. At 20 cm it was the same size. The sign of m tells whether the image is erect or inverted.
The magnification produced by a lens 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 of a lens: m = h′/h = v/u.
Check yourself
How is the magnification of a lens defined?
An object is at u = −15 cm and a convex lens forms its image at v = +30 cm. Use m = v/u to find m.
Answer: -2
m = v/u = (+30 cm)/(−15 cm) = −2.
An object 2.0 cm tall has a magnification m = −2 in a lens. What is the image height h′ in cm?
Answer: -4 cm
h′ = m h = (−2)(2.0 cm) = −4.0 cm: the image is 4 cm tall and inverted.
Which expression gives the magnification produced by a lens?
- The ratio of the focal length to the object distance. Magnification compares the heights of the image and the object. The distances enter in m = v/u.
- The ratio of the height of the image to the height of the object — correct. Yes!
- The difference between the image height and the object height. Magnification is a ratio, found by dividing, not by subtracting.
- −v/u. That is the expression for a spherical mirror. For a lens, m = v/u.
- u/v. That is v/u turned upside down. The image distance goes on top.
- v/u — correct. Yes!