# lensmaker formula

The formula (at the bottom of this post) shows for thin, spherical lenses the relationship between shape and power.

Be d center thickness of the lens element.
and be the radii of the spheres that describe the surfaces.
Keep the sign conventions for radii in mind, however!

be the index of refraction of the medium outside the lens and
n be the index of refraction of the lens material.

f be the focallength of the lens and
D be it’s Power,

For spherical optical systems holds generally in the paraxial region:

Is the surrounding medium air, we get (because ) the approximation:

Are the lenses also thin (idealizing ), the formula simplifies to
Lensmaker’s formula: