Lens Maker Equation Calculator
Calculate focal length of lenses using the lens maker equation with precise optical parameters
Calculate Lens Focal Length
Left surface radius (positive for convex from left)
Right surface radius (negative for convex from right)
Use 0 for thin lens approximation
Material refractive index (glass ≈ 1.5)
Lens Calculation Results
Focal Length
Lens Properties
Formula used: 1/f = (n-1) × (1/R₁ - 1/R₂)
Sign convention: Cartesian (positive = center of curvature on right side)
Lens Analysis
Example Calculation
Double Convex Glass Lens
Radius 1 (R₁): +10 cm (convex from left)
Radius 2 (R₂): -10 cm (convex from right)
Lens thickness: 0 cm (thin lens)
Refractive index: 1.5 (crown glass)
Calculation Steps
1/f = (n-1) × (1/R₁ - 1/R₂)
1/f = (1.5-1) × (1/0.1 - 1/(-0.1))
1/f = 0.5 × (10 - (-10))
1/f = 0.5 × 20 = 10
f = 0.1 m = 10 cm
Sign Convention
Positive Radius
Center of curvature on right
Convex from left side
Negative Radius
Center of curvature on left
Concave from left side
Common Lens Materials
Design Tips
Positive focal length = converging lens
Negative focal length = diverging lens
Higher refractive index = shorter focal length
Thickness affects thick lens behavior
Power (D) = 1/focal length (m)
Understanding the Lens Maker Equation
What is the Lens Maker Equation?
The lens maker equation relates the focal length of a lens to its physical properties: the refractive index of the material and the radii of curvature of its surfaces. This fundamental equation is essential for designing optical systems.
Applications
- •Eyeglass lens design
- •Camera lens systems
- •Telescope and microscope optics
- •Laser beam shaping
- •Optical instrument design
Mathematical Formulation
Thin lens: 1/f = (n-1) × (1/R₁ - 1/R₂)
Thick lens: 1/f = (n-1) × (1/R₁ - 1/R₂ + (n-1)×d/(n×R₁×R₂))
- f: Focal length
- n: Refractive index of lens material
- R₁: Radius of curvature (first surface)
- R₂: Radius of curvature (second surface)
- d: Lens thickness
Key Insight: The focal length depends on both the lens shape (curvature) and the material properties (refractive index).
Lens Types and Configurations
Biconvex
R₁ > 0, R₂ < 0 - Strong converging lens with symmetric curvatures
Plano-Convex
R₁ > 0, R₂ = ∞ - Moderate converging lens with one flat surface
Biconcave
R₁ < 0, R₂ > 0 - Diverging lens with inward-curved surfaces