Lens Maker's Equation (solved for $f$ $f$ )

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Nov 7, 2024, 4:04:48 PM

Created by

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Jun 17, 2016, 3:37:34 PM

f = {[(\frac{n_{lens}}{n_{medium}} - 1) (\frac{1}{r_{1}} - \frac{1}{r_{2}})]}^{- 1}

$f = [(n_"lens"/n_"medium" - 1) ( 1/r_1 - 1/r_2)]^(-1)$

(nlens)Lens Refraction Index.

$(n_"lens")"Lens Refraction Index."$

(nmedium)Surrounding Medium Refraction Index.

$(n_"medium")"Surrounding Medium Refraction Index."$

(r_{1}) Lens Curvature Radius toward Light Source.

$(r_1)"Lens Curvature Radius toward Light Source."$

(r_{2}) Lens Curvature Radius away from Light Source.

$(r_2)"Lens Curvature Radius away from Light Source."$

The Math / Science

This Lens Maker's Equation¹(solved for $f$ $f$ ) calculates the focal length of a lens given its geometry and surroundings. For more information on and versions of the Lens Maker's Equation, please see the Lens Maker's Equation Calculator page.

Lens Maker's Equation:

$f = {[(\frac{n_{lens}}{n_{medium}} - 1) (\frac{1}{r_{1}} - \frac{1}{r_{2}})]}^{- 1}$ $f = [(n_"lens"/n_"medium" - 1)(1/r_1 - 1/r_2)]^-1$

where:

f is the focal length of the lens
n_lens is the index of refraction of the lens. For more information on the index of refraction, click here.
n_medium is the index of refraction of the material surrounding the lens.
r₁ is the radius of lens curvature of the side nearest the "object" ( the source of the light rays).
r₂ is the radius of lens curvature of the side farthest from the object.

Related Calculators:

Compute the focal length of a lens
Compute the index of refraction of a lens
Compute the index of refraction of the material surrounding a lens given that lens's geometry and surroundings.
Compute the radius of curvature of the side of a lens that faces away from the object
Compute the radius of curvature of the object-facing side of a lens

^ Walker, Jearl, David Halliday, and Robert Resnick. "Images." Fundamentals of Physics. 8E ed. Hoboken, NJ: Wiley, 2008. 936. Print.

This equation, Lens Maker's Equation (solved for

f

$f$ ), is used in 3 pages

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Lens Maker's Equation (solved for ff)

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Lens Maker's Equation (solved for $f$ $f$ )