Lens Formula, Magnification and Power

Calculating where the image forms.

Using the Cartesian sign convention, distances are measured from the optical centre and are positive in the direction of the incoming light. The lens formula then links object distance, image distance and focal length. Magnification is the image distance divided by the object distance.

The power of a lens is the reciprocal of its focal length in metres and is measured in dioptres. A convex lens has positive power and a concave lens negative power. Lenses placed together add their powers.

• Negative magnification means an inverted image.
• Spectacle prescriptions are quoted in dioptres.
• A 0.5 m focal length gives 2 dioptres.

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