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

Enter a value for all fields

The Radius of Curvature of a Lens away from Light Source calculator  computes the radius of curvature (r₂) based on its geometry and material index of the lens and surrounding material.

INSTRUCTIONS: Choose units and enter the following:

• (n_lens)  Refraction Index of Lens Material.
• (n_medium)  Refraction Index of Surrounding Material.
• (r₁)  Radius of Curvature of Lens Toward Light Source.
• (f) Focal Length of Lens.

Radius of Curvature(r₂):  The calculator returns the radius in meters.  However, this can be automatically converted to other length units via the pull-down menu.

The Math / Science

This Lens Maker's Equation¹(solved for `r_2`) calculates the radius of curvature of the side of a lens that faces away from the object, 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 = [(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 

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