What is the Lens Maker's Formula Calculator?
Quick Answer: A tool that computes the focal length (f) of a thin lens from its refractive index (n) and the radii of curvature (R1, R2) of its two surfaces using the lens maker's formula: 1/f = (n - 1)(1/R1 - 1/R2). It also shows a schematic lens shape based on the signs of R1 and R2.
Theory of the Lens Maker's Formula
The Lens Maker's Formula relates the focal length of a thin lens in air to its refractive index and surface curvatures. For a lens in air, the formula is:
1/f = (n - 1) * (1/R1 - 1/R2)
where:
- n is the refractive index of the lens material (relative to air).
- R1 is the radius of curvature of the first surface (positive if center of curvature is on the outgoing side).
- R2 is the radius of curvature of the second surface (positive if center of curvature is on the incoming side? Standard sign convention: R1 positive if surface is convex towards the incident light; R2 positive if surface is convex towards the incident light? We'll use the Cartesian sign convention: incident light from left to right. For a surface, radius is positive if center of curvature is to the right. Thus for a biconvex lens, R1 > 0, R2 < 0. For a biconcave lens, R1 < 0, R2 > 0.)
The calculator uses this formula exactly. It also sketches a simple lens profile illustrating the curvature signs.
Step-by-Step Examples
Example 1: Biconvex Lens
- Set n = 1.5, R1 = +20 cm, R2 = -20 cm. Click Calculate.
- Result: f = +20 cm. The lens is converging.
- Observe the diagram: both surfaces bow outward (convex).
Example 2: Biconcave Lens
- Change R1 = -20 cm, R2 = +20 cm. Then f = -20 cm (diverging).
- The diagram shows inward curving surfaces.
Example 3: Plano‑convex Lens
- Set R1 = +20 cm, R2 = Infinity (enter a large number like 10000). f = +40 cm (since (1/infinity)=0).
Frequently Asked Questions
What sign convention is used for radii?
Cartesian sign convention (light travels left to right). R1 is positive if the center of curvature is to the right of the first surface. R2 is positive if the center of curvature is to the right of the second surface (i.e., the second surface is convex towards the right). In practice, for a biconvex lens, R1 > 0, R2 < 0. For a biconcave lens, R1 < 0, R2 > 0.
Why does the lens shape change when I change signs?
The shape is drawn based on the signs of R1 and R2. Positive R corresponds to a convex surface (bulging outward), negative R corresponds to a concave surface (caving inward).
What if one radius is infinity?
Enter a very large number (e.g., 10000) to approximate a plane surface. The term 1/R becomes zero, simulating a plano lens.
Is the lens assumed to be in air?
Yes, the formula applies for a lens in air. If the lens is in a medium other than air, the refractive index should be the relative index (n_lens / n_medium).
Can I calculate n or R if f is known?
This version only calculates f. For solving other variables, you would need to rearrange the formula manually or use a dedicated solver.