What thin lens equation does this calculator solve?

It solves the thin lens equation 1/f = 1/do + 1/di, where f is the focal length, do the object distance and di the image distance. Give it any two and it returns the third. For example, a converging lens with f = 10 cm and an object at do = 30 cm gives 1/di = 1/10 - 1/30 = 1/15, so di = 15 cm. Leave the box you want solved empty; the other two drive the result.

How do object distance, image distance and focal length relate?

They are tied together by the reciprocals: 1/f equals 1/do plus 1/di. Move the object farther out and the image pulls closer to the focal point; bring it inside the focal length on a converging lens and the image flips to the same side and becomes virtual. With f = 10 cm, an object at 20 cm (that is 2f) puts the image at 20 cm the same size, which is the symmetric case worth memorizing.

How is magnification m = -di/do interpreted?

Magnification is m = -di/do. The sign tells orientation and the size tells scale. A value like m = -0.5 (from di = 15, do = 30) means the image is inverted and half the height of the object. A positive m means upright, an |m| above 1 means enlarged, below 1 means reduced. Multiply m by the object height to get the image height: a 4 cm object at m = -0.5 forms a 2 cm tall inverted image.

How do I tell a real image from a virtual image?

Read the sign of the image distance. A positive di means a real image forming on the far side of the lens that you can catch on a screen, like the inverted picture a projector throws. A negative di means a virtual image on the same side as the object that only appears to be there, like the upright enlarged view through a magnifying glass when the object sits inside the focal length.

What is the sign convention for convex and concave lenses?

This tool uses the common real-is-positive convention. A converging convex lens has a positive focal length; a diverging concave lens has a negative focal length, such as f = -10 cm. Object distances are positive for a normal object in front of the lens. A diverging lens always produces a virtual, upright, reduced image: feed f = -10 and do = 20 and you get di near -6.67 cm with m about 0.33.

What happens when the object sits exactly at the focal point?

When do equals f, the rays leave the lens parallel and meet only at infinity, so there is no finite image distance. The calculator detects this and tells you the image is at infinity instead of dividing by zero. This is the principle behind a collimator and the reason a slide projector goes out of focus as you slide the film toward the focal plane of the lens.

Check homework on the thin lens equation

A physics problem gives a converging lens of focal length 10 cm and an object 30 cm away, then asks for the image distance and whether the image is real or inverted. Type f = 10 and do = 30, leave di blank, and read di = 15 cm, m = -0.5, real and inverted and half-size. You confirm your algebra in one step instead of re-deriving the reciprocals by hand, and the labels match the wording the textbook uses to grade the answer.

Set up a projector or camera distance

You know the lens focal length and how far the screen sits, and you want the object distance that brings the image into focus. Enter f and the image distance di, leave do blank, and the tool solves the object distance for you. Because the equation is symmetric, the same trick finds the film to lens spacing in a camera once you fix the subject distance.

Explain magnifying glasses to a class

To show why a magnifier makes things bigger, put the object inside the focal length: f = 10 cm and do = 5 cm. The tool returns di = -10 cm and m = 2, tagged virtual, upright and enlarged. Project the URL on the board and students see the negative image distance is exactly what makes the image virtual, which lands better than a paragraph of prose.

Compare converging and diverging lenses

Hold the object fixed at 20 cm and flip the focal length sign. With f = 10 cm you get a real inverted image; with f = -10 cm the same object gives di near -6.67 cm, a virtual upright reduced image. Putting the two runs side by side makes the role of the sign convention concrete instead of abstract, which is the part students most often get backwards.

Lens Equation Calculator — Thin Lens 1/f = 1/do + 1/di

Solve 1/f = 1/do + 1/di — enter any two of focal length, object and image distance, get the third plus magnification and a real/virtual verdict, browser-only

Runs locally
Category Calculator
Best for Getting a realistic range before a purchase, plan, workout, or schedule decision.

Enter any two of focal length, object distance and image distance — leave the third box empty and it is solved from 1/f = 1/do + 1/di. Sign convention: a converging (convex) lens has f > 0, a diverging (concave) lens f < 0; a positive image distance is a real image, a negative one is virtual. Magnification is m = -di/do.

Leave one box blank — that is the unknown.

Focal length f (cm)

Object distance do (cm)

Image distance di (cm)

= 15

Object height (optional)Used only to scale the image height.

Result

Focal length f

Object distance do

Image distance di

Magnification m

-0.5

Lens

converging (convex)

real imageinvertedreduced

What this tool does

A thin lens equation calculator that solves 1/f = 1/do + 1/di for whichever value you leave blank. Type any two of focal length, object distance and image distance, and the tool returns the third, the lateral magnification m = -di/do, the image height if you supply an object height, and a plain reading of the image: real or virtual, upright or inverted, enlarged or reduced. It uses the standard real-is-positive convention from intro optics, so a converging convex lens has a positive focal length and a diverging concave lens a negative one, while a negative image distance flags a virtual image you cannot project on a screen. Edge cases are handled honestly: put the object at the focal point and it tells you the image goes to infinity rather than printing a meaningless number. Every result is one click to copy, and the focal length, object and image distances ride in the URL so a worked example shares as a link. Everything runs in your browser with no upload.

Tool details

Input: Numbers; The page exposes text boxes, numeric controls, file pickers, or structured inputs depending on the tool.
Output: Live result + Copy; The result area focuses on usable output, with copy, download, or preview actions when supported.
Privacy: Browser-side processing; The main tool logic does not call an external API, so inputs normally stay in the current tab.
Save / share: Shareable URL state; Key settings are encoded in the URL so another person can reopen the same setup.
Performance budget: Initial JS <= 9 KB; No WASM budget is declared, keeping the tool quick to open on mobile.
Best fit: Calculator · Student; Category and role tags drive related tools, internal links, and quick fit checks.

How to use

1. Input

Paste or drop your content into the tool panel.
2. Process

Click the button. All processing is local in your browser.
3. Copy / Download

Copy the result or download to disk in one click.

How Lens Equation Calculator fits into your work

Use it for fast estimates, comparisons, and planning numbers before you make the final call.

Calculation jobs

Getting a realistic range before a purchase, plan, workout, or schedule decision.
Comparing scenarios by changing one input at a time.
Turning rough assumptions into a number you can discuss.

Calculation checks

Double-check units, dates, rates, and rounding assumptions.
Treat health, finance, tax, and legal outputs as planning aids, not professional advice.
Save the inputs that produced an important result so you can reproduce it later.

Good next steps

These links move the current task into a more complete workflow.

Real-world use cases

Check homework on the thin lens equation
A physics problem gives a converging lens of focal length 10 cm and an object 30 cm away, then asks for the image distance and whether the image is real or inverted. Type f = 10 and do = 30, leave di blank, and read di = 15 cm, m = -0.5, real and inverted and half-size. You confirm your algebra in one step instead of re-deriving the reciprocals by hand, and the labels match the wording the textbook uses to grade the answer.
Set up a projector or camera distance
You know the lens focal length and how far the screen sits, and you want the object distance that brings the image into focus. Enter f and the image distance di, leave do blank, and the tool solves the object distance for you. Because the equation is symmetric, the same trick finds the film to lens spacing in a camera once you fix the subject distance.
Explain magnifying glasses to a class
To show why a magnifier makes things bigger, put the object inside the focal length: f = 10 cm and do = 5 cm. The tool returns di = -10 cm and m = 2, tagged virtual, upright and enlarged. Project the URL on the board and students see the negative image distance is exactly what makes the image virtual, which lands better than a paragraph of prose.
Compare converging and diverging lenses
Hold the object fixed at 20 cm and flip the focal length sign. With f = 10 cm you get a real inverted image; with f = -10 cm the same object gives di near -6.67 cm, a virtual upright reduced image. Putting the two runs side by side makes the role of the sign convention concrete instead of abstract, which is the part students most often get backwards.

Common pitfalls

Forgetting the sign convention. A converging convex lens has a positive focal length and a diverging concave lens a negative one. Entering a concave lens as f = 10 instead of f = -10 flips real to virtual and inverts the orientation, so the whole verdict comes out wrong.
Reading a negative image distance as an error. A negative di is not a bug; it means the image is virtual and on the same side as the object, the normal result for a magnifying glass or any diverging lens. Take the sign as information, not a mistake.
Filling in all three boxes. The tool solves for the one value you leave blank, so if focal length, object distance and image distance are all entered there is nothing left to solve. Clear whichever quantity you want the calculator to find.

Privacy

Every calculation here is plain JavaScript that runs inside your browser tab. The focal length, object and image distances you type are never sent to a server, and nothing is logged. The one thing to know: the shareable link encodes those three numbers in the query string, so a link pasted into chat will record them in the recipient server access log. For routine optics homework that is harmless, but if the values are confidential use the copy button and paste the text rather than sharing the URL.

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Lens Equation Calculator — Thin Lens 1/f = 1/do + 1/di

What this tool does

Tool details

How to use

1. Input

2. Process

3. Copy / Download

How Lens Equation Calculator fits into your work

Calculation jobs

Calculation checks

Good next steps

Real-world use cases

Check homework on the thin lens equation

Set up a projector or camera distance

Explain magnifying glasses to a class

Compare converging and diverging lenses

Common pitfalls

Privacy

FAQ

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