Lensmaker's Equation

\frac{1}{f} = (n-1)\left(\frac{1}{R_1} - \frac{1}{R_2}\right)

Relates the focal length of a lens to its refractive index and surface curvatures.

Variables

Focal length

Refractive index of lens

Allowed values: 1 or more

unitless

R₁

Radius of first surface

R₂

Radius of second surface

Your notes

0/5000

Check value

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n = 1.5 (Refractive index of lens)
R₁ = 3 m (Radius of first surface)
R₂ = 4 m (Radius of second surface)

Result: f = 24 m

Other optics formulas with the same quantities

Lens Power (Lenses) shares Focal length
Mirror Equation (Reflection) shares Focal length
Focal Length and Radius (Reflection) shares Focal length
F-Number (f-stop) (Optical Instruments) shares Focal length
Depth of Field (Optical Instruments) shares Focal length
Spherical Mirror Focal Length (Reflection) shares Focal length

Where this formula is listed

Optics formulas, under Lenses, alongside Lens Magnification and Combined Lens Power.
In the optics list it comes after Thin Lens Equation and before Lens Magnification.
Optics formula sheet, one of 34 formulas printed with symbol keys and SI units.
The full formula index, grouped by category and topic.

Common questions

What is the Lensmaker's Equation formula?

Lensmaker's Equation is written 1/f = (n − 1)(1/R₁ − 1/R₂). Relates the focal length of a lens to its refractive index and surface curvatures. It belongs to Optics, under Lenses.

What are the units in 1/f = (n − 1)(1/R₁ − 1/R₂)?

In SI units, f is focal length, measured in m; n is refractive index of lens (dimensionless); R₁ is radius of first surface, measured in m; R₂ is radius of second surface, measured in m.