Lambda Physics

Optical Coatings Research Laboratory

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Image Distance and Magnification Calculator

Calculate where a thin-lens image will form from the object distance and lens focal length. The calculator also determines image magnification, whether the image is real or virtual, whether it is upright or inverted, and automatically distinguishes converging and diverging lenses.

Thin-lens image formation

Input parameters
Applied formulas
1/f = 1/do + 1/di
di = f do / (do − f)
m = −di / do
Using the standard thin-lens sign convention.

Calculation results

Image distance di
–
distance from lens to image
Magnification m
–
negative = inverted, positive = upright
Converging / Diverging Lens
Real / Virtual Image
Upright / Inverted Image
Schematic image formation
Interpretation: A positive focal length represents a converging lens; depending on object position it can form a real or virtual image. A negative focal length represents a diverging lens, which for a real object forms a virtual, upright, reduced image. When do = f for a positive focal length, the image is formed at infinity.

Thin-lens image distance calculation

This free online calculator uses the thin-lens equation to determine the image distance from the object distance and focal length of a lens.

It also calculates the transverse magnification and identifies the image as real or virtual and upright or inverted according to the sign of the calculated image distance and magnification. Positive focal length denotes a converging lens; negative focal length denotes a diverging lens.

Typical uses

The calculator is useful for basic optical experiments, lens testing, imaging setups, projection systems and educational demonstrations of geometrical optics.

Related optical calculations

For a given object and image distance, the complementary Lens Focal Length Calculator can be used to determine the focal length experimentally.

More free optical calculators are available in the Lambda Physics Optical Calculations collection.

Lambda Physics also offers optical components and materials in its General Stock.