Lens Maker's Calculator Formula for Distance

Lens Maker's Formula:

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

Focal Length (f):

1. What is the Lens Maker's Formula?

Definition: This formula relates the focal length of a lens to its refractive index and the radii of curvature of its surfaces.

Purpose: It helps opticians and lens designers calculate the focal length of lenses for glasses, cameras, telescopes, and other optical devices.

2. How Does the Formula Work?

The formula is:

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

Where:

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

Sign Convention:

Convex surface: Positive radius
Concave surface: Negative radius
Flat surface: Infinite radius (enter 0 in calculator)

3. Importance of Lens Calculations

Details: Accurate focal length calculation is essential for proper vision correction, camera lens design, and scientific instruments.

4. Using the Calculator

Tips:

Enter refractive index (typically 1.5 for glass)
Enter radii of curvature with correct sign (+/-)
For flat surfaces, enter 0
All values must be valid numbers

5. Frequently Asked Questions (FAQ)

Q1: What's a typical refractive index for lenses?
A: Glass lenses are typically 1.5-1.9, plastics 1.49-1.74, depending on material.

Q2: How do I determine the radius of curvature?
A: For existing lenses, use a lens measure tool. For new designs, it's determined by desired optical properties.

Q3: What if one surface is flat?
A: Enter 0 for the flat surface's radius (1/∞ = 0).

Q4: Why does the formula have (n - 1)?
A: This accounts for the refractive index difference between lens material and surrounding medium (typically air, n≈1).

Q5: Can this calculate lens power in diopters?
A: Yes, lens power (P) in diopters is simply 1/f where f is in meters.