Thin Lens Calculator
Calculate image distance and magnification using the thin lens equation 1/f = 1/dₒ + 1/dᵢ. Find image type (real/virtual, upright/inverted), lens power in diopters, and two-lens system focal length.
Image Distance dᵢ (cm)
—
Magnification m —
Image Type —
Lens Power (diopters, if f in m) —
Extended More scenarios, charts & detailed breakdown ▾
Image Distance dᵢ (cm)
—
Magnification m —
Image Height hᵢ (cm) —
Image Type —
Professional Full parameters & maximum detail ▾
Image Properties
Image Distance dᵢ (cm) —
Image Height hᵢ (cm) —
Image Type —
Magnification
Lateral Magnification m —
Longitudinal Magnification m² —
Lens Power
Lens Power P (diopters) —
How to Use This Calculator
- Enter focal length f (positive for converging/convex, negative for diverging/concave).
- Enter object distance dₒ (always positive — distance from object to lens).
- Results show image distance, magnification, and image type.
- Use Find Focal Length tab if you know both distances.
- Use Two-Lens System for combined focal length of two lenses.
Formula
Thin Lens Equation: 1/f = 1/dₒ + 1/dᵢ
Magnification: m = −dᵢ/dₒ = hᵢ/hₒ
Lens Power: P = 1/f(m) = 100/f(cm) diopters
Two lenses: 1/f = 1/f₁ + 1/f₂ − d/(f₁f₂)
Example
Example: f = 10 cm, dₒ = 30 cm. 1/dᵢ = 1/10 − 1/30 = 2/30. dᵢ = 15 cm. m = −15/30 = −0.5 (real, inverted, half-size). P = 100/10 = +10 D.
Frequently Asked Questions
- 1/f = 1/dₒ + 1/dᵢ, where f = focal length, dₒ = object distance, dᵢ = image distance. A positive dᵢ means a real image on the opposite side from the object; negative means a virtual image on the same side.
- m = −dᵢ/dₒ. If |m| > 1, the image is larger; |m| < 1 means smaller. Negative m = inverted image (real); positive m = upright image (virtual for a converging lens).
- P = 1/f where f is in meters. So f = 10 cm = 0.10 m → P = +10 D. Eyeglass prescriptions use diopters; positive = converging (farsighted correction), negative = diverging (nearsighted correction).
- When dₒ = f, the image is at infinity — refracted rays are parallel. This is how lenses collimate light in projectors and flashlights.
- For two thin lenses separated by distance d: 1/f = 1/f₁ + 1/f₂ − d/(f₁f₂). If d = 0 (touching), it simplifies to P_total = P₁ + P₂.
Related Calculators
Sources & References (5) ▾
- Thin Lens Equation — HyperPhysics — Georgia State University
- OpenStax University Physics Vol 3, Ch 2.4 — Thin Lenses — OpenStax
- Hecht, E. Optics (5th ed.) — Pearson
- MIT OCW 8.03 Vibrations and Waves — Geometric Optics — MIT OpenCourseWare
- University of Rochester Optical Sciences — Lens Tutorials — University of Rochester