Lens Magnification Calculator
Find the magnification M, image distance, and whether the image is real or virtual, inverted or upright — for any converging or diverging thin lens.
cm
cm
Inverted and diminished image
- 1
Denominator (dₒ − f)
30 − 10 = 20 cm - 2
Image distance dᵢ
10 × 30 ÷ (20) = 15 cmRearrangement of 1/f = 1/dₒ + 1/dᵢ gives dᵢ = f·dₒ/(dₒ − f). - 3
Magnification M
−(15) ÷ 30 = -0.5000
How does this calculator work?
Thin lens: dᵢ = f·dₒ/(dₒ−f) then M = −dᵢ/dₒ. M < 0 → inverted; M > 0 → upright; |M| > 1 → magnified; |M| < 1 → diminished; dᵢ > 0 → real image; dᵢ < 0 → virtual. Object must not be placed exactly at the focal point.
Formula
How this is calculated
The thin-lens equation 1/f = 1/dₒ + 1/dᵢ links the focal length f, the object distance dₒ (object to lens), and the image distance dᵢ (lens to image). Rearranging gives dᵢ = f·dₒ/(dₒ − f). For a converging (convex) lens f is positive; for a diverging (concave) lens f is negative. Object distance must always be positive (object in front of the lens).
The linear magnification M = −dᵢ/dₒ describes the image relative to the object. A positive M means the image is upright; negative M means it is inverted. |M| > 1 means magnified, |M| < 1 means diminished. A positive dᵢ places the image on the far side of the lens (real image, projectable on a screen); a negative dᵢ means a virtual image on the same side as the object.
When dₒ equals f, refracted rays are parallel and the image is at infinity — no finite image exists, and the calculator shows a warning. This model uses the paraxial approximation (small angles, thin lens); thick-lens or wide-angle scenarios require additional corrections.
Frequently asked questions
M < 0 means the image is inverted (upside-down) relative to the object. This is typical for real images formed by a converging lens when the object is beyond the focal point.
A real image (dᵢ > 0) forms where actual light rays converge on the far side of the lens — it can be projected onto a screen. A virtual image (dᵢ < 0) forms where diverging rays appear to come from, on the same side as the object; a screen placed there shows nothing.
A magnifying glass is a converging lens with the object inside the focal length (dₒ < f). This gives a positive, upright, virtual image with M > 1 — the enlarged image appears on the same side as the object.
Also known as
TG we-Calculate Editorial Team. (2026). Lens Magnification Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/lens-magnification-calculator
TG we-Calculate Editorial Team. "Lens Magnification Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/lens-magnification-calculator.
TG we-Calculate Editorial Team, "Lens Magnification Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/lens-magnification-calculator
@misc{wecalculate_lens_magnification_calculator, title = {Lens Magnification Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/lens-magnification-calculator}}, year = {2026}, note = {TG we-Calculate} }
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