The Scale of Vision
Magnification ($M$) is the process of enlarging the apparent size, not the physical size, of something. In optics, it is a dimensionless number that tells you how much larger (or smaller) an image appears compared to the original object.
This calculator uses the standard definitions for thin lenses and spherical mirrors, allowing you to calculate magnification either from the heights of the object and image, or from their distances relative to the lens/mirror.
Understanding the Sign Convention
The sign of the magnification is just as important as the number itself:
- Positive ($+$): The image is upright (right-side up) and is considered a "virtual" image.
- Negative ($-$): The image is inverted (upside down) and is considered a "real" image.
- $|M| > 1$: The image is enlarged.
- $|M| < 1$: The image is reduced.
The Formula
Example Calculation
You look at a $5 , \text{cm}$ ($0.05 , \text{m}$) tall bug through a magnifying glass. The virtual image appears to be $15 , \text{cm}$ ($0.15 , \text{m}$) tall.
- Divide Image Height by Object Height: $0.15 / 0.05 = 3$.
The magnifying glass has a magnification of $3\text{x}$. The positive sign indicates the image is upright.