Physics & Mechanics

Magnification Calculator

Calculate the magnification of a lens or mirror based on object distance and image distance, or object height and image height.

m
m
m
m
Magnification (M)
-2
Image TypeInverted / Real

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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

M=hiho=dido\begin{aligned} M = \frac{h_i}{h_o} = -\frac{d_i}{d_o} \end{aligned}

Where:
M=
Magnification
hih_i=
Image Height
hoh_o=
Object Height
did_i=
Image Distance
dod_o=
Object Distance

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.

  1. 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.

Frequently Asked Questions

The negative sign ensures the mathematical conventions remain consistent. In a single-lens system, if the image distance ($d_i$) is positive (a real image), the light has crossed over the focal point, meaning the image must be upside down (negative magnification).

Theoretically, yes. If you place an object exactly at the focal point of a converging lens, the image forms at infinity. The light rays become perfectly parallel, and the apparent size is infinitely large (though in reality, lens imperfections limit this).

While linear magnification (calculated here) compares physical heights on a focal plane, angular magnification compares the angle an object takes up in your field of vision with and without an optical instrument like a telescope.