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Thin Lens Equation Calculator

Solve for a lens's focal length, object distance, or image distance using 1/f = 1/do + 1/di, plus magnification and whether the image is real or virtual.

Focal length
10 cm
Object distance
30 cm
Image distance
15 cm
Magnification
-0.5×
Image type
Real (light actually converges here — can be projected on a screen)
Orientation
Inverted

How it works

The thin lens equation, 1/f = 1/do + 1/di, relates a lens's focal length (f) to the distance from the lens to the object (do) and the distance from the lens to the image it forms (di). Pick which one to solve for; the calculator rearranges the same identity to find it from the other two.

This uses the standard real-is-positive sign convention: a positive image distance means a real image (light actually converges there — it could be projected on a screen), while a negative image distance means a virtual image (light only appears to diverge from there, the way a magnifying glass works when the object is closer than the focal length). Magnification is m = −di/do — negative means the image is upside down (inverted), and |m| greater than 1 means it's enlarged.

Because every term in the equation is 1/length, the formula only cares that focal length, object distance, and image distance all share the same unit — it works out identically whether that unit is centimeters or inches, so no internal metric/imperial conversion happens before the formula runs.

FAQ

Why did the image distance come out negative?

A negative image distance means the image is virtual — it forms on the same side of the lens as the object, which happens whenever the object is placed closer to the lens than its focal length. You can't project a virtual image on a screen; it's what you see when you look through the lens, the way a magnifying glass or a camera's viewfinder works.

What does a magnification greater than 1 mean?

The image is larger than the object — a magnification of 2× means the image is twice the object's height. A magnification between 0 and 1 means the image is smaller than the object, and the sign (positive or negative) separately tells you whether it's upright or inverted.

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