Free · Optics and light calculators 🔍

Thin Lens Image Distance and Magnification

Solve signed image and focal distances, positive real-object distance and magnification magnitude with independent length units and editable inverses.

  • Formula & worked example
  • Private in your browser
  • No signup
Go to tool

Calculator inputs

Loading calculator…

How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

A converging thin lens with a 5 cm focal length and an object 10 cm away forms a real image 10 cm on the other side. Its magnification magnitude is 1; the image is inverted.

1/f = 1/do + 1/di; M = |di|/do. Positive di means a real image; negative di means a virtual image.

Worked example

Enter these known values and leave the other values blank.

Real-object distance
10 cm
Signed focal length
5 cm
Signed image distance
10 cm
Magnification magnitude
1

Assumptions and limitations

  • This is the thin, paraxial lens model with the same surrounding medium on both sides. Distances are measured from the lens plane. Thickness, aberrations and large-angle rays are not modeled.
  • The object must be real with strictly positive distance. Focal length is positive for a converging lens and negative for a diverging lens. Image distance is positive on the outgoing side for a real image and negative on the incoming side for a virtual image.
  • Magnification here is a positive size ratio, not signed orientation. A positive image distance gives an inverted real image; a negative image distance gives an upright virtual image. Signed transverse magnification would be −di/do.
  • Enter two compatible distances to solve the third and magnification. Image distance plus magnitude also recovers positive object distance. Magnification alone does not choose the sign of an image distance; the captured graph does not supply that ambiguous inverse.
  • An object exactly at the focal point has an image at infinity. An image exactly at the focal point requires an infinitely distant object. Equal and opposite object and image distances require infinite focal length. These limits remain unknown with an explanation instead of a finite result.
  • All four quantities remain editable and support locks. The three distance controls each retain 11 unit choices, including feet/inches and meters/centimeters. A negative mixed value places the minus sign on the first component, such as −0:50 for negative 50 cm.
  • Zero distances and zero magnification are outside this finite real-object model. Missing inputs remain incomplete. Locked inconsistent values produce a conflict. Results are an ideal optical estimate rather than a complete lens design.

Common questions

Can the image distance be negative?

Yes. A negative distance identifies a virtual image on the object side of the lens. For a real object its image is upright.

What happens when the object is closer than a converging lens’s focal length?

The signed image distance is negative and the image is virtual and enlarged. With f = 5 cm and do = 3 cm, di = −7.5 cm and the magnitude is 2.5.

Does magnification tell me whether an image is inverted?

This magnitude is unsigned. Use the image-distance sign: positive indicates an inverted real image, while negative indicates an upright virtual image for this real-object model.

Why is the result blank at the focal point?

The outgoing rays are parallel and the image distance is infinite. A finite numerical image distance cannot describe that limit.

References

Preserve both captured equations and all five inverse branches, guarding exactly zero denominators so infinite-distance limits remain unknown instead of producing nonfinite results. Magnification alone does not determine the image-distance sign. Restrict this magnitude model to finite, positive real-object distances and positive magnification. Retain signed nonzero focal lengths and virtual-image distances, with explicit errors for focal-point and infinite-focal-length geometries.

Explore optics and light calculators 🔍 or browse all physics calculators.