1. What is the Lens Maker's Formula?

The Lens Maker's Formula 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 and lens manufacturing.

2. How Does the Calculator Work?

The calculator uses the Lens Maker's formula:

Where:

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

Sign Convention:

• For convex surfaces (bulging out), radius is positive
• For concave surfaces (caving in), radius is negative
• For flat surfaces, radius is infinity (1/R = 0)

3. Importance of Focal Length Calculation

Details: The focal length determines the lens's optical power and how it bends light. Accurate calculation is essential for designing optical systems like cameras, telescopes, and eyeglasses.

4. Using the Calculator

Tips: Enter refractive index (must be >1), and radii of curvature (positive for convex, negative for concave). Remember the sign convention for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What is the refractive index of common lens materials?
A: Glass ~1.5-1.9, Plastics ~1.49-1.74, Diamond ~2.42. The refractive index varies with wavelength.

Q2: How does surface curvature affect focal length?
A: More curved surfaces (smaller radius) create stronger lenses with shorter focal lengths.

Q3: What if one surface is flat?
A: For a flat surface (R=∞), its 1/R term becomes zero in the formula.

Q4: Can this formula be used for thick lenses?
A: The formula assumes thin lenses. For thick lenses, additional factors must be considered.

Q5: What if both surfaces have the same curvature?
A: If R₁ = R₂, the lens becomes a concentric shell with special optical properties.