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Electrical & Computer Engineering
Integrated Microfabrication Lab
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Thin Lens Equations & Calculators

The position, orientation, and size of an image formed by a lens are determined by two things: the focal length of the lens and the position of the original object. The focal length of a lens is determined by two things itself: the radius of curvature of the lens and the index of refraction of the material of which the lens is made. Below is an equation known as the Lens Maker's Formula.

Lens Maker's Formula
Lens maker's formula diagram

Where:

n1 = index of refraction of a lens
n0 = index of refraction of the medium surrounding the lens - usually air (n0=1)
R1 = radius of curvature of the front surface
R2 = radius of curvature of the second surface
f = Focal Length

NOTE: The sign convention used is as follows: if R1 is positive, the first surface is convex, and if R1 is negative, the surface is concave. The signs are reversed for the back surface of the lens: if R2 is positive, the surface is concave, and if R2 is negative, the surface is convex.


Lens maker's formula inputs



Thin Lens Equation
Thin lens equation diagram

Where:

DI = Distance between the image and the center of the lens
DO = Distance between the object and the center of the lens
F = Focal length

NOTE: The sign convention used is as follows: if DI is negative then the image produced is a virtual image on the same side of the lens as the object itself.


Thin lens equation inputs