Lens Maker's Equation Calculator
Enter the refractive index and the two surface radii (in meters) to find the focal length and optical power of a lens using the lens maker's equation.
How to use the lens maker's equation calculator
- Enter the refractive index of the lens material (greater than 1).
- Enter the radius of the first and second surfaces in meters, using the sign convention.
- Read the focal length in meters and the optical power in diopters.
Examples
Symmetric biconvex lens
n = 1.5, R1 = 0.1 m, R2 = -0.1 m
1/f = 0.5 x (10 - (-10)) = 10, so f = 0.1 m and power = 10 D
Plano-convex lens (one flat side)
n = 1.5, R1 = 0.2 m, R2 = Infinity (flat)
1/f = 0.5 x (5 - 0) = 2.5, so f = 0.4 m and power = 2.5 D
Frequently asked questions
What is the lens maker's equation?
It gives the focal length of a thin lens from its material and shape: 1/f = (n - 1)(1/R1 - 1/R2), where n is the refractive index and R1, R2 are the surface radii.
What sign convention does this use?
A surface that bulges toward the incoming light has a positive radius; one that curves away has a negative radius. Convex toward the source is positive.
How do I enter a flat surface?
A flat surface has an infinite radius, so enter Infinity. Its term 1/R becomes zero, which is correct for a plano lens.
What is optical power in diopters?
Power is the reciprocal of the focal length in meters, P = 1/f. A lens with a 0.5 m focal length has a power of 2 diopters.
Why must the refractive index be greater than 1?
The factor (n - 1) would be zero or negative otherwise, so a lens with n of 1 or less has no focusing power. Both surfaces being flat is also rejected.
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