Thin Lens & Mirror Equation Calculator
Solve the thin lens and mirror equation for any one unknown and find the magnification and image type.
Solve for
Optic type
cm
cm
Real image
- 1
1/f − 1/dₒ
1 ÷ 10 − 1 ÷ 30 = 0.066667From 1/f = 1/dₒ + 1/dᵢ, rearranged to give 1/dᵢ = 1/f − 1/dₒ. - 2
Image distance dᵢ = 1 ÷ (1/f − 1/dₒ)
1 ÷ 0.066667 = 15
How does this calculator work?
Enter any two of focal length, object distance, and image distance (in cm) and pick the unknown. The calculator applies 1/f = 1/do + 1/di to solve for the third value, then computes magnification m = -di/do and flags whether the image is real or virtual and upright or inverted.
Formula
How this is calculated
The thin lens (and spherical mirror) equation relates the focal length f, the object distance do, and the image distance di by 1/f = 1/do + 1/di. Enter any two of these three quantities in centimeters and choose which one to solve for. Rearranging gives di = 1/(1/f - 1/do), f = 1/(1/do + 1/di), and do = 1/(1/f - 1/di).
The magnification is m = -di/do. A negative magnification means the image is inverted (a real image for a single converging lens), while a positive magnification means it is upright. The magnitude |m| tells you how many times larger or smaller the image is than the object. With the convention used here, a positive focal length describes a converging lens or concave mirror.
Sign convention matters: for a lens a positive image distance (di > 0) indicates a real image formed on the opposite side from the object, while a negative di indicates a virtual image on the same side. Distances are in centimeters, but any consistent length unit works since the equation is scale-free. Watch for the edge case where 1/f - 1/do = 0 (object at the focal point), which sends the image to infinity and makes the result undefined.
Frequently asked questions
A positive focal length means a converging lens or concave mirror. A positive image distance corresponds to a real image, and a positive magnification means the image is upright.
When the object sits exactly at the focal point (do = f), the term 1/f - 1/do becomes zero and the image forms at infinity, so the calculator cannot return a finite value.
A negative magnification indicates the image is inverted relative to the object, which for a single converging lens corresponds to a real image.
Also known as
TG we-Calculate Editorial Team. (2026). Thin Lens & Mirror Equation Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/thin-lens-mirror-calculator
TG we-Calculate Editorial Team. "Thin Lens & Mirror Equation Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/thin-lens-mirror-calculator.
TG we-Calculate Editorial Team, "Thin Lens & Mirror Equation Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/thin-lens-mirror-calculator
@misc{wecalculate_thin_lens_mirror_calculator, title = {Thin Lens & Mirror Equation Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/thin-lens-mirror-calculator}}, year = {2026}, note = {TG we-Calculate} }
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