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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. Now 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 Forumla

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.


Index of refraction of the lens (n1): Radius of curvature (R1 in mm)
Index of refraction of the surrounding medium (n0): Radius of Curvature (R2 in mm)

Focal Length (in mm):



Thin Lens Equation

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.


Object Distance (DO):
Focal Length (F):

Image Distance (DI):
Magnification: