Biconvex Lens
Converging(( ))
Both surfaces curve outward. Most common converging lens.
Parameters
R₁ = +10 cm
R₂ = −10 cm
n = 1.5
f = +10 cm
Applications
Magnifying glassesCamera lensesEyeglasses for farsightedness
Lens Examples
Explore different lens types with detailed calculations using the lens maker formula. Each example includes real-world applications and typical parameter values.
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Converging Lenses (f > 0)
- • Biconvex: R₁ > 0, R₂ < 0
- • Plano-convex: R₁ > 0, R₂ = ∞ (or vice versa)
- • Positive Meniscus: Both radii same sign, |R₁| < |R₂|
Diverging Lenses (f < 0)
- • Biconcave: R₁ < 0, R₂ > 0
- • Plano-concave: R₁ < 0, R₂ = ∞ (or vice versa)
- • Negative Meniscus: Both radii same sign, |R₁| > |R₂|
Biconcave Lens
Diverging)( )(
Both surfaces curve inward. Common diverging lens.
Parameters
R₁ = −10 cm
R₂ = +10 cm
n = 1.5
f = −10 cm
Applications
Eyeglasses for nearsightednessLaser beam expandersPeepholes
Plano-convex Lens
Converging| )
One flat surface, one convex surface.
Parameters
R₁ = +20 cm
R₂ = ∞
n = 1.5
f = +40 cm
Applications
FlashlightsCondenser lensesLaser focusing
Plano-concave Lens
Diverging| (
One flat surface, one concave surface.
Parameters
R₁ = −20 cm
R₂ = ∞
n = 1.5
f = −40 cm
Applications
Beam expansionOptical instrumentsProjection systems
Positive Meniscus
Converging( (
Both surfaces curve same direction, but converging.
Parameters
R₁ = +10 cm
R₂ = +20 cm
n = 1.5
f = +40 cm
Applications
Corrective eyewearCamera accessoriesOptical correction
Negative Meniscus
Diverging) )
Both surfaces curve same direction, but diverging.
Parameters
R₁ = +20 cm
R₂ = +10 cm
n = 1.5
f = −40 cm
Applications
EyeglassesOptical systemsBeam shaping
Detailed Calculation Example
Problem: Design a biconvex lens with f = 5 cm
Given: Glass with n = 1.52, equal radii of curvature (|R₁| = |R₂| = R)
Step 1: Apply the formula with R₁ = +R, R₂ = −R
1/f = (n − 1)(1/R₁ − 1/R₂)
1/0.05 = (1.52 − 1)(1/R − 1/(−R))
20 = 0.52 × (2/R)
Step 2: Solve for R
R = 2 × 0.52 / 20 = 0.052 m = 5.2 cm
Result: Use R₁ = +5.2 cm, R₂ = −5.2 cm
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