# Thin Lens Equation Calculator

Calculate image distance, magnification, and image type using the thin lens equation. Supports converging and diverging lenses.

## What this calculates

The thin lens equation 1/f = 1/dₒ + 1/dᵢ relates the focal length of a lens to the object and image distances. This calculator determines where the image forms, its magnification, and whether it is real or virtual, upright or inverted. It works for both converging (positive f) and diverging (negative f) lenses.

## Inputs

- **Focal Length (f)** (cm) — Positive for converging, negative for diverging lens
- **Object Distance (dₒ)** (cm) — min 0
- **Object Height** (cm)

## Outputs

- **Image Distance (dᵢ)** (cm) — Positive = real image, Negative = virtual image
- **Magnification** — M = -dᵢ/dₒ (negative = inverted image)
- **Image Height** (cm) — Height of the image
- **Image Type** — formatted as text — Real/Virtual, Upright/Inverted

## Frequently Asked Questions

**Q: What is the thin lens equation?**

A: The thin lens equation is 1/f = 1/dₒ + 1/dᵢ, where f is the focal length, dₒ is the object distance from the lens, and dᵢ is the image distance. It applies when the lens thickness is small compared to the focal length, object distance, and image distance.

**Q: What is the difference between a real and virtual image?**

A: A real image forms where light rays actually converge and can be projected onto a screen (positive dᵢ). A virtual image forms where light rays appear to diverge from (negative dᵢ) and cannot be projected onto a screen. You see a virtual image when looking through a magnifying glass at an object closer than the focal length.

**Q: What does negative magnification mean?**

A: Negative magnification means the image is inverted (upside down) relative to the object. Positive magnification means the image is upright. The absolute value of magnification gives the size ratio: |M| > 1 means the image is larger than the object, |M| < 1 means it is smaller.

**Q: When does a converging lens produce a virtual image?**

A: A converging (convex) lens produces a virtual image when the object is placed between the focal point and the lens (dₒ < f). In this case, the lens acts as a magnifying glass, producing an upright, enlarged, virtual image. When the object is beyond the focal point, a real, inverted image is formed.

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Source: https://vastcalc.com/calculators/physics/thin-lens
Category: Physics
Last updated: 2026-04-21