Lens and Mirror Equation Calculator
An object 15 cm from a converging lens of focal length 10 cm forms an image at 30 (cm, same unit as the inputs): real, inverted and twice the size.
Converging lens or concave mirror: positive. Diverging lens or convex mirror: negative.
30 m
- In cm
- 3000 cm
- In mm
- 30000 mm
- In km
- 0.03 km
- In in
- 1181.102362 in
- In ft
- 98.42519685 ft
- Magnification m = −dᵢ/dₒ
- -2
- Image
- real, inverted, enlarged
- Power 1/f (f in metres)
- 0.1 D (dioptres)
Step-by-step solution
- dᵢ = 1 ÷ (1 ÷ f − 1 ÷ dₒ)
- dᵢ = 1 ÷ (1 ÷ 10 − 1 ÷ 15)
- dᵢ = 30 m
Lens and Mirror Equation Formula
1/f = 1/dₒ + 1/dᵢ, m = −dᵢ/dₒ
f focal length, dₒ object distance, dᵢ image distance (real-is-positive convention); m magnification
Worked Example
An object 15 cm from a converging lens with f = 10 cm:
- dᵢ = 1 ÷ (1 ÷ f − 1 ÷ dₒ)
- dᵢ = 1 ÷ (1 ÷ 10 − 1 ÷ 15)
- dᵢ = 30 m
In mm: 30000 mm · In km: 0.03 km · In in: 1181.102362 in · In ft: 98.42519685 ft · Magnification m = −dᵢ/dₒ: -2 · Image: real, inverted, enlarged · Power 1/f (f in metres): 0.1 D (dioptres)
Where the image goes
Object beyond 2f: real, inverted, reduced (a camera). Between f and 2f: real, inverted, enlarged (a projector). Inside f: virtual, upright, enlarged (a magnifying glass).
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Frequently asked questions
Which sign convention does this use?
Real-is-positive: real objects and images have positive distances; virtual images negative; converging lenses and concave mirrors have positive f. In the Cartesian (NCERT) convention, 1/v − 1/u = 1/f for lenses: put dₒ = −u and dᵢ = v and it is the same equation.
Does it work for mirrors?
Yes. The mirror equation has the same form, with f = R/2. A real image forms in front of a mirror, so treat it as positive here.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). Lens and Mirror Equation Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/lens-equation-calculator/
IEEE
Scientific Converters, "Lens and Mirror Equation Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/lens-equation-calculator/