Magnification Formula
Calculate how much a lens or mirror enlarges or reduces an image.
Used in microscopy, photography, and telescope design.
The Formula
M = -dᵢ / dₒ = hᵢ / hₒ
Magnification tells you how much larger or smaller the image is compared to the object. A negative magnification means the image is inverted (flipped upside down).
Variables
| Symbol | Meaning |
|---|---|
| M | Magnification (unitless ratio) |
| dᵢ | Image distance from the lens or mirror |
| dₒ | Object distance from the lens or mirror |
| hᵢ | Height of the image |
| hₒ | Height of the object |
Example 1
Object is 20 cm from a lens, image forms at 40 cm. Find the magnification.
M = -dᵢ / dₒ = -40 / 20
M = -2 (image is twice as large and inverted)
Example 2
A 5 cm tall object produces a 2 cm tall image. Find the magnification.
M = hᵢ / hₒ = 2 / 5
M = 0.4 (image is 40% of the original size, upright)
When to Use It
Use the magnification formula when:
- Determining how much a microscope or telescope enlarges an image
- Calculating image size in camera and projector systems
- Finding whether an image will be upright or inverted
- Designing optical instruments with specific zoom levels