Lens Maker Equation Calculator Software

Lens Maker's Equation:

\[ \frac{1}{f} = (n - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) \]

Refractive Index (n):

(dimensionless)

Radius of First Surface (R₁):

meters

Radius of Second Surface (R₂):

meters

Focal Length (f):

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1. What is the Lens Maker's Equation?

The Lens Maker's Equation relates the focal length of a lens to its refractive index and the radii of curvature of its two surfaces. It's fundamental in optical design for determining how a lens will focus light.

2. How Does the Calculator Work?

The calculator uses the Lens Maker's equation:

\[ \frac{1}{f} = (n - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) \]

Where:

\( f \) — Focal length of the lens (meters)
\( n \) — Refractive index of the lens material (dimensionless)
\( R_1 \) — Radius of curvature of the first surface (meters)
\( R_2 \) — Radius of curvature of the second surface (meters)

Sign Convention:

For convex surfaces (bulging outward), radius is positive
For concave surfaces (curving inward), radius is negative
For flat surfaces, radius is considered infinite (∞)

3. Importance of Focal Length Calculation

Details: Accurate focal length calculation is crucial for designing optical systems like cameras, telescopes, eyeglasses, and microscopes. It determines how light rays converge or diverge when passing through the lens.

4. Using the Calculator

Tips:

Enter refractive index (must be ≥1)
Enter radii in meters (use positive for convex, negative for concave)
For plano-convex or plano-concave lenses, enter ∞ for the flat side (or leave one field blank)
The calculator will compute the focal length in meters

5. Frequently Asked Questions (FAQ)

Q1: What is the sign convention for radii?
A: Convex surfaces (bulging outward) have positive radii, concave surfaces (curving inward) have negative radii.

Q2: How do I represent a flat surface?
A: For a flat surface, the radius is infinite (∞). In practice, you can leave one radius field blank or enter a very large number.

Q3: What are typical refractive index values?
A: Common values: ~1.5 for glass, ~1.33 for water, ~1.0 for air. High-index lenses for glasses may go up to 1.74.

Q4: What if I get a negative focal length?
A: A negative focal length indicates a diverging (concave) lens, while positive indicates converging (convex).

Q5: Does this work for thick lenses?
A: This equation assumes thin lenses. For thick lenses, additional factors must be considered.