Object Distance Calculator

Calculator Inputs

Optical Setup

Converging setups use positive focal length. Diverging setups use negative focal length internally.

Focal Length

Image Distance Magnitude

Image Nature

Real images are treated as positive image distances. Virtual images are treated as negative.

Distance Unit

Decimal Places

Object Height (Optional)

Image Height (Optional)

Graph Max Image Distance

Object Distance Graph

The line shows how object distance magnitude changes with image distance magnitude for the current setup and image type.

Example Data Table

Case	Setup	Focal Length	Image Distance	Image Nature	Object Distance	Magnification
1	Converging Lens	10 cm	15 cm	Real	30 cm	-0.5
2	Converging Lens	12 cm	24 cm	Real	24 cm	-1.0
3	Diverging Lens	-8 cm	-6 cm	Virtual	24 cm	0.25
4	Converging Mirror	20 cm	30 cm	Real	60 cm	-0.5
5	Diverging Mirror	-15 cm	-10 cm	Virtual	30 cm	0.3333

Formula Used

This calculator uses the thin optics relationship between focal length, image distance, and object distance. Signed values are applied internally.

1 / f = 1 / v - 1 / u

1 / u = 1 / v - 1 / f

u = 1 / [(1 / v) - (1 / f)]

Where:

f = signed focal length
v = signed image distance
u = signed object distance
m = magnification = v / u
P = optical power in diopters = 1 / f in meters

Converging setups use positive focal length. Diverging setups use negative focal length. Real images are positive. Virtual images are negative.

How to Use This Calculator

Select the optical setup that matches your lens or mirror.
Enter the focal length as a positive magnitude in your preferred unit.
Enter the image distance magnitude and choose whether the image is real or virtual.
Optionally add object height or image height for magnification checks.
Choose decimal precision and an optional graph range.
Press the calculate button to show the result above the form.
Review the graph, derived quantities, and worked steps.
Download the result as CSV or PDF when needed.

Frequently Asked Questions

1. What does object distance mean here?

It is the distance from the optical element to the object position. The calculator reports both the signed value and the absolute distance magnitude.

2. Why do I choose real or virtual image?

That choice sets the image-distance sign. Real images use positive image distance. Virtual images use negative image distance in this calculator.

3. Can I use this for mirrors and lenses?

Yes. The setup menu supports converging and diverging lenses, plus converging and diverging mirrors, using the same signed thin-optics equation.

4. Why does the calculator show a negative object distance?

A negative signed value usually represents a real object under the chosen sign convention. The magnitude box shows the ordinary positive distance size.

5. What happens if image distance equals focal length?

The denominator becomes zero, which means the object is effectively at infinity. The calculator asks you to change the inputs.

6. How is magnification calculated?

Magnification is computed from distance values using m = v / u. Negative magnification means inverted orientation. Positive magnification means upright orientation.

7. Are the height inputs required?

No. They are optional. Use them when you want estimated image height, estimated object height, or a check against height-based magnification.

8. Does the graph use my current setup?

Yes. The curve uses your focal length, image type, units, and graph range to plot how object distance changes across image distances.