Thin lens equation calculator

Formula

How it works

The thin lens equation relates the focal length, the object's distance from the lens, and the image's distance. A positive image distance means a real image forms on the far side of the lens; a negative one means a virtual image forms on the same side as the object. Magnification compares the image's height with the object's.

Worked example

The same calculation with the default values:

• Focal length 10 cm
• Object distance 30 cm

1. 1 ÷ dᵢ = 1 ÷ 10 − 1 ÷ 30 → dᵢ = 15
2. m = −15 ÷ 30 = -0.5

Result: Image distance: 15 cm · Magnification: -0.5 · Image type: Real (forms on the far side of the lens)

Common mistakes

• Mixing up the sign convention - this calculator follows a specific convention for object/image distance signs (real vs virtual images), and plugging in values with the opposite sign convention gives a wrong image position or magnification.
• Forgetting that a negative magnification means the image is inverted, not that it's somehow a negative-size image.
• Applying the thin-lens equation to a thick lens or a compound lens system - it is only accurate for an idealized thin lens.