Lens Maker Equation Calculator

The lens maker's equation (thin lens form) is:

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

Where:

• f — focal length of the lens
• n — refractive index of the lens material
• n_m — refractive index of the surrounding medium (1.0 for air, 1.33 for water)
• R₁ — radius of curvature of the front (first) surface
• R₂ — radius of curvature of the back (second) surface

The sign convention for radii follows the standard rule:

• R > 0 if the center of curvature is to the right (convex surface facing the incoming light)
• R < 0 if the center of curvature is to the left (concave surface facing the incoming light)
• R = ∞ for a flat surface (use a very large number)

Common lens configurations:

• Biconvex: R₁ > 0, R₂ < 0 → converging
• Biconcave: R₁ < 0, R₂ > 0 → diverging
• Plano-convex: R₁ > 0, R₂ = ∞ → converging
• Meniscus: Both R same sign — converging or diverging depending on which |R| is smaller

The optical power P = 1/f (in diopters when f is in meters) is useful for comparing lenses. In optometry, lens prescriptions are given in diopters because the powers of thin lenses in contact add algebraically: P_total = P₁ + P₂.

This equation assumes a thin lens — one whose thickness is negligible compared to the radii of curvature and focal length. For thick lenses, a more complete version includes a term proportional to the lens thickness divided by the product of the refractive index and the radii.

The focal length is the key output: positive means converging, negative means diverging. The optical power in diopters equals 1/f(meters) — higher values mean stronger converging or diverging action. The lens type confirms whether your surface curvatures and material produce a converging or diverging lens.

To change the surrounding medium from air (n_m = 1.0) to water (n_m = 1.33), expand the advanced settings. Immersing a glass lens in water significantly increases its focal length because the refractive index ratio decreases.