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Magnification (Lens or Mirror)

Magnification tells you how many times bigger or smaller an image is compared to the original object. It is the image height divided by the object height, which also equals the image distance divided by the object distance. A positive magnification means the image is upright; a negative value means it is inverted (upside down). For example, a magnification of 2 means the image is twice as tall as the object. This is used in designing cameras, telescopes, and eyeglasses.

Written by the Vorzep Team

Optics Geometric Optics Imaging

⟹ Solve⟷m, d_i, d_o

m (magnification)

dimensionless

d_i (image)

d_o (object)

Please fix the errors above.

Solve for: m d_i d_o

Presets:

m—

—

m: —d_i: —d_o: —

✓ Copied!

Magnification (m) Gauge—

Upright (m > 0) Inverted (m < 0) Same size (m = ±1)

m = −dᵢ / dₒ · Positive m = upright image, Negative m = inverted image · Distances in consistent units

Variables

Symbol	Quantity	Unit
m	Magnification
d_i	Image distance	cm
d_o	Object distance	cm

What it means

Magnification is the ratio of the image size to the object size. For lenses and mirrors, it is the negative of the ratio of image distance to object distance (using sign conventions). A positive m indicates an upright image; negative indicates inverted. This formula is used in microscopy, telescopy, photography, and any imaging system to predict image size. Understanding magnification helps in designing optical instruments and in interpreting images.

Worked example

Magnification – Two Detailed Examples

Real‑World

Scenario: A camera lens forms a real image at a distance d_i = 30 cm from the lens, while the object is 15 cm from the lens. The photographer calculates the magnification m = −d_i/d_o = −30/15 = −2. The negative sign indicates an inverted image, and the magnitude 2 means the image is twice the size of the object. This tells them the subject will appear larger on the sensor, which is useful for macro photography.

Parameter	Value
d_i (cm)	30
d_o (cm)	15

1m = −30 / 15 = −2

Result −2 ✓ Inverted, magnified 2×

Scenario: A concave mirror produces a virtual image with d_i = −20 cm (behind the mirror) when the object is 20 cm in front. The magnification m = −(−20)/20 = 1. This indicates an upright image of the same size as the object. This is typical for plane mirrors and certain concave mirror configurations (object at centre of curvature). The engineer uses this to design an optical system where image size equals object size.

Parameter	Value
d_i	−20
d_o	20

1m = −(−20) / 20 = 1

Result 1 ✓ Upright, same size

Insight: Magnification indicates the size and orientation of the image. A negative value means inverted; positive means upright. Magnitude greater than 1 means enlarged, less than 1 means reduced.

Common mistakes

Magnification (lens or mirror): m = −d_i / d_o – the negative sign indicates image orientation.
Sign: |m| > 1 means magnified; |m| < 1 means reduced. A negative m means inverted image; positive m means upright.
d_i and d_o: Use signed distances according to the sign convention.
Units: d_i and d_o in the same units – m is dimensionless.
Lateral vs. angular magnification: This is lateral (transverse) magnification – different from angular magnification (e.g., magnifying glass).

Applications

Magnification (lens or mirror), m = −d_i/d_o, gives the lateral magnification, where d_i and d_o are image and object distances. The negative sign indicates inverted images. Engineers and opticians use this to calculate the size of images, to design optical systems for desired magnification, and to specify lenses for cameras and microscopes. By understanding magnification, they can ensure that the final image meets resolution and size requirements. This formula is also used in machine vision to calibrate systems. It is a key parameter in both geometrical and optical design, enabling the prediction of how objects will appear after passing through a lens or reflecting off a mirror.

Design of magnifiers, microscopes, and telescopes
Camera lens selection and system calibration
Optical projection systems (slides, cinema)
Image size calculations in machine vision
Educational understanding of image scaling and inversion

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Published July 13, 2026
Last updated September 28, 2026