Refraction Through Lenses
Simple Explanation
As light passes through a lens, it refracts at both curved surfaces, ultimately forming an image that can be real or virtual, and larger, smaller, or the same size as the object — the magnification formula quantifies exactly how much larger or smaller the image is.
Why Do We Need It?
Understanding image formation — not just WHERE an image forms (the lens equation) but also its SIZE and orientation (magnification) — is essential for fully predicting what a lens does to an object being viewed or projected.
Formula
Linear Magnification (Lens)
m = v/u
Magnification compares the size of the image produced by a lens to the size of the original object, using the ratio of image distance to object distance.
- m
- — Magnification (no units) — |m| > 1 means the image is larger than the object
- v
- — Image distance from the lens
- u
- — Object distance from the lens
When to use it: Use to find how much larger or smaller an image is compared to the original object, once v and u are known.
Worked Example
Finding magnification
A lens forms an image at v = 15 cm from an object at u = -30 cm. Find the magnification.
Why Does This Work?
Magnification directly compares how far the image forms from the lens to how far the object is from the lens — this ratio captures the geometric similarity between the triangles formed by the object, image, and the lens's optical centre, which is why it directly gives the image-to-object size ratio.
Real-Life Example
A magnifying glass
Holding a magnifying glass close to small text makes it appear much larger.
When the object is closer to the lens than its focal length, the lens produces a virtual, upright, and magnified (|m| > 1) image — this is exactly the configuration used when reading with a magnifying glass.
Practice
A lens forms an image at v = 40 cm from an object at u = -10 cm. Find the magnification.
MediumCommon mistake
Ignoring the SIGN of the magnification, only considering its size — a negative magnification indicates an inverted image, while a positive magnification indicates an upright image; both the magnitude and sign carry important information.
Quick Review
- m = v/u gives the magnification (image size relative to object size).
- |m| > 1 means enlarged; |m| < 1 means reduced.
- Negative m means inverted image; positive m means upright image.