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Index of Refraction of a Lens

n_{lens} = n_{medium} ⎡ ⎢ ⎣ \frac{1}{(\frac{1}{r_{1}} - \frac{1}{r_{2}}) f} + 1 ⎤ ⎥ ⎦

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

(nmedium) Index of refraction of the medium surrounding the lens

$(n_"medium")" Index of refraction of the medium surrounding the lens"$

(f) Focal length of the lens

$(f)"Focal length of the lens "$

(r_{1}) Radius of curvature of lens toward light source.

$(r_1)"Radius of curvature of lens toward light source."$

(r_{2}) Radius of curvature of lens farthest from light source.

$(r_2)"Radius of curvature of lens farthest from light source."$

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The Index of Refraction of a Lens calculator /attachments/29ec1675-395d-11e6-9770-bc764e2038f2/lens.png computes the index of refraction of a lens (n_lens) based on its geometry and surroundings.

INSTRUCTIONS: Choose units and enter the following:

(n_medium) Refraction Index of Surrounding Material.
(r₁) Radius of Curvature of Lens Toward Light Source.
(r₂) Radius of Curvature of Lens Away from Light Source.
(f) Focal Length of Lens.

Refraction Index (n_lens): The calculator returns the refraction index.

The Math / Science

This Lens Maker's Equation^{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.