Thin Lens Calculator
Find the image distance di from a thin lens using 1/f = 1/do + 1/di. Enter focal length and object distance to locate the image. Positive di means a real image; negative means virtual.
How to use this tool
- Enter focal length (f) and object distance (do) in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your image distance (di) and the full breakdown beneath it.
Formula
1/f = 1/do + 1/di → di = 1 / (1/f − 1/do)
How it works
Rearrange the thin-lens equation: 1/di = 1/f − 1/do, then take the reciprocal.
Worked example
Common mistakes to avoid
- Using the wrong sign for focal length — converging (convex) lenses have a positive f; diverging (concave) lenses have a negative f. Getting this wrong flips the image position.
- Entering object distance as a negative number when using the real-is-positive sign convention — object distance do is positive when the object is on the incoming light side of the lens.
- Confusing di with the distance from the object to the screen — di is measured from the lens, not from the object.
Key terms
Frequently asked questions
- What does a negative image distance di mean?
- A negative di indicates a virtual image, located on the same side of the lens as the object. Virtual images cannot be projected onto a screen but can be seen by looking through the lens (as with a magnifying glass).
- What happens when the object is placed at the focal point (do = f)?
- The formula gives 1/di = 1/f - 1/f = 0, meaning di is infinite. The refracted rays emerge parallel and never converge to form an image, which is why a flashlight uses a bulb placed at the focal point to produce a parallel beam.
- How do I find the magnification after using this calculator?
- Magnification m = -di / do. A positive m means the image is upright; negative means inverted. |m| > 1 means the image is larger than the object.