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

Enter a value for all fields

The Radius of Curvature of a Lens toward Light Source calculator  computes the radius of curvature (r₁) 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.
• (r₂)  Radius of Curvature of Lens Away from Light Source.
• (f) Focal Length of Lens.

Radius of Curvature(r₁):  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_1`) calculates the radius of curvature of the object-facing side 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 = [(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.