Image Distance Calculator

Calculator

Optical element

Uses the same equation for thin lenses and spherical mirrors.

Solve for

Switch this to compute any missing variable.

Units

All distances must use the same unit.

Sign mode

Easy mode treats do as a magnitude.

Rounding (0–12)

Controls displayed decimals and exports.

Focal length f

Use negative f for diverging elements.

Object distance do

Easy mode converts this to a positive magnitude.

Image distance di

Needed only when solving for f or do.

Reset

Example data table

Element	f	do	Computed di	Interpretation
Lens (converging)	10 cm	30 cm	15 cm	Real, inverted, diminished
Lens (diverging)	-10 cm	30 cm	-7.5 cm	Virtual, upright, diminished
Mirror (converging)	12 cm	24 cm	24 cm	Real, inverted, same size
Mirror (diverging)	-12 cm	24 cm	-8 cm	Virtual, upright, diminished

These rows are examples to help you test the calculator.

Formula used

The calculator uses the thin lens / spherical mirror equation: 1/f = 1/do + 1/di

f = focal length
do = object distance
di = image distance
m = −di/do = magnification

If di is positive, the image is real; if negative, it is virtual. Use “Signed inputs” if you follow a strict sign convention in your coursework.

How to use this calculator

Select lens or mirror, then choose what you want to solve.
Pick a unit and keep all distances in that unit.
Enter two known values; leave the target value as any number.
Use negative focal length for diverging elements.
Press Calculate to see results, steps, and classification.
Use the download buttons to export CSV or PDF.

FAQs

1) What does a negative image distance mean?

A negative di indicates a virtual image. Virtual images form where rays appear to meet, not where they physically converge, so they cannot project on a screen.

2) When should focal length be negative?

Use negative focal length for diverging elements, like a concave lens or a convex mirror. This helps the equation predict a virtual image in many common setups.

3) Why does the result show infinity sometimes?

If 1/di becomes zero, di is infinite. That happens when the object is at the focal point, producing parallel rays and an image at infinity.

4) Can I mix units like cm and m?

No. Keep f, do, and di in the same unit. The equation is unit-consistent, but mixing units will produce incorrect values.

5) What is magnification and what does its sign mean?

Magnification is m = −di/do. A negative m indicates an inverted image. A positive m indicates an upright image. The magnitude shows how much larger or smaller the image is.

6) Does this work for thick lenses?

This tool uses the thin-lens approximation. For thick lenses, principal planes shift, and you may need a more detailed model or manufacturer lens data.

7) How do I interpret results for mirrors?

The same equation is used. A positive di usually implies a real image in front of the mirror. A negative di implies a virtual image behind the mirror.

8) What should I do if I use a different sign convention?

Switch to “Signed inputs” and enter signed values consistently. The calculator will compute the missing variable and magnification based on your provided signs.