Thin Lens Calculator
A negative image distance is a magnifying glass, not an error.
Work out Thin Lens. A negative image distance is a magnifying glass, not an error. States the assumption instead of hiding it.
Positive for a converging lens, negative for a diverging one.
Image distance
0.15 m
Real, inverted and reduced — the camera case
The thin lens equation is 1/f = 1/u + 1/v, and the sign convention is what confuses everyone. Object distance is positive, focal length is positive for a converging lens and negative for a diverging one, and a positive image distance means the image forms on the far side. A negative image distance is a virtual image on the same side as the object. That is not an error — it is exactly what a magnifying glass produces when the object sits inside the focal length, and it is why you cannot project the enlarged image onto a screen. Optical power in dioptres is the reciprocal of focal length in metres, which is how spectacles are prescribed. A +2.00 lens has a 500 mm focal length, and the reason powers are used rather than focal lengths is that they add when lenses are combined.
How the Thin Lens Calculator works
Image position, size and orientation from the thin lens equation, with the sign convention stated. A negative image distance means a virtual image on the same side as the object, which is exactly what a magnifying glass produces.
Also known as: where does the image form · 1/f = 1/u + 1/v calculator · magnification of a lens · why is my image virtual
Frequently asked questions
What is the thin lens equation?
1/f = 1/u + 1/v, where u is the object distance, v the image distance and f the focal length. It assumes the lens is thin enough that its thickness can be ignored.
What does a negative image distance mean?
A virtual image, on the same side as the object. It cannot be projected onto a screen but you can see it by looking through the lens — which is what happens with a magnifying glass or a diverging lens.
Why does my magnifying glass sometimes flip the image?
Because you moved past the focal length. Inside it the image is virtual, upright and enlarged; outside it the image becomes real and inverted, which is the same lens obeying the same equation.
What is a dioptre?
The reciprocal of focal length in metres, and how spectacles are prescribed. A +2.00 lens has a 500 mm focal length. Powers are used because they add when lenses are combined, while focal lengths do not.
What happens at exactly the focal point?
No image forms. The rays emerge parallel and meet only at infinity, which is why the equation divides by zero there and this calculator declines to answer.
Put this calculator on your own site
Free to use, on any site, commercial or not. Paste this where you want it to appear. It is a plain iframe, so it works in WordPress, Squarespace, Wix, Webflow, Ghost and anything else that accepts HTML.
<iframe src="https://www.thecalclibrary.com/embed/lens-equation-calculator" width="100%" height="640" style="border:1px solid #e2e8f0;border-radius:12px" loading="lazy" title="Thin Lens Calculator"></iframe>
<p style="font:13px/1.5 system-ui,sans-serif;margin:6px 0 0;color:#64748b">Powered by <a href="https://www.thecalclibrary.com/lens-equation-calculator" style="color:#64748b">Thin Lens Calculator</a> from The Calc Library</p>The only condition is that the credit line below the frame stays in place. That one line is what pays for the tool being free — it is how anyone else finds it.