๐ Thin Lens Equation Calculator
Any consistent unit works (cm, mm, etc.) โ just use the same unit for both values.
Enter a lensโs focal length and the object distance to calculate the image position (image distance) and magnification using the thin lens equation (1/f=1/do+1/di). Use a positive focal length for a converging (convex) lens and a negative one for a diverging (concave) lens.
How to use
- Enter the focal length (positive for convex, negative for concave).
- Enter the object distance (distance from the lens to the object, always positive).
- The image distance, magnification, real/virtual, and upright/inverted status are calculated automatically.
How the calculation works
For a lens thin enough that its thickness can be ignored, this tool works out where the image forms and how large it is. Lens equation: 1/f = 1/do + 1/di Magnification: m = โdi รท do f is the focal length, do the distance from the lens to the object and di the distance from the lens to the image. Enter f as positive for a converging (convex) lens and negative for a diverging (concave) lens. A positive image distance means a real image on the far side of the lens, where light actually meets and can be caught on a screen. A negative one means a virtual image that you can only see by looking through the lens. A negative magnification means the image is upside down; positive means upright. If the object sits exactly at the focal point, the light leaves in parallel and no image forms, so no result is shown.
Worked example
A convex lens with f = 10 cm and the object at 30 cm 1/di = 1/10 โ 1/30 = 2/30 โ image distance 15 cm Magnification: โ15 รท 30 = โ0.5 (real, inverted, half size) A convex lens with f = 10 cm and the object at 5 cm (a magnifying glass) Image distance โ10 cm, magnification 2 (virtual, upright, twice the size) A concave lens with f = โ10 cm and the object at 30 cm Image distance โ7.5 cm, magnification 0.25 (virtual, upright, reduced)
Things to be aware of
- The formula does not apply directly to thick lenses or to camera lenses made of several elements.
- With a convex lens, an object beyond twice the focal length gives a smaller real image, exactly at twice gives the same size, and between f and 2f gives a larger real image.
- Any length unit works (cm, mm and so on), as long as the focal length and object distance use the same one.
FAQ
What sign convention does this use?
It uses the โreal is positiveโ convention: object distance is always positive, image distance is positive for a real image and negative for a virtual one, and focal length is positive for a converging lens and negative for a diverging lens.
What does a virtual image mean?
A negative image distance means the image is virtual โ light rays donโt actually converge there, so it canโt be projected onto a screen (like the image seen through a magnifying glass or mirror).
What does a negative magnification mean?
A negative magnification means the image is inverted (upside down and reversed) relative to the object. A positive magnification means the image is upright.