1. What is the Lensmaker's Equation?

The Lensmaker's Equation relates the focal length of a lens to its refractive index and the radii of curvature of its surfaces. It's fundamental in optical design and lens manufacturing.

2. How Does the Calculator Work?

The calculator uses the Lensmaker's Equation:

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:

• R is positive for convex surfaces (when light hits them first)
• R is negative for concave surfaces (when light hits them first)
• R is infinite (∞) for flat surfaces

3. Importance of Focal Length Calculation

Details: Accurate focal length calculation is crucial for designing optical systems, eyeglasses, cameras, telescopes, and other lens-based devices.

4. Using the Calculator

Tips:

• Enter refractive index (must be > 1)
• Enter radii in meters (use positive for convex, negative for concave)
• For a flat surface, enter a very large number (e.g., 99999)

5. Frequently Asked Questions (FAQ)

Q1: What is a typical refractive index for lenses?
A: Common values: 1.5 (crown glass), 1.6-1.7 (high-index glass), ~1.49 (acrylic plastic).

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

Q3: What's the difference between R₁ and R₂?
A: R₁ is the first surface light encounters, R₂ is the second surface. Order matters in the calculation.

Q4: Can this be used for thick lenses?
A: This is the thin lens approximation. For thick lenses, additional factors must be considered.

Q5: What if I get a negative focal length?
A: Negative focal length indicates a diverging (concave) lens, while positive indicates converging (convex).