1. What is the Lens Equation?

The lens equation (1/f = 1/do + 1/di) relates the focal length (f) of a lens to the distances of the object (do) and the image (di) from the lens. It's fundamental in geometric optics for thin converging lenses.

2. How Does the Calculator Work?

The calculator uses the lens equation:

Where:

• \( f \) — Focal length of the lens (m)
• \( d_o \) — Object distance from lens (m)
• \( d_i \) — Image distance from lens (m)

Explanation: The calculator solves for whichever parameter is left blank when the other two are provided. It automatically rearranges the equation to solve for the missing variable.

3. Importance of Lens Calculations

Details: Accurate lens calculations are essential for designing optical systems, understanding image formation, and predicting the behavior of light through lenses in cameras, microscopes, eyeglasses, and other optical devices.

4. Using the Calculator

Tips: Enter any two known values (f, do, or di) in meters, leaving the third field blank. The calculator will compute the missing value. All inputs must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between converging and diverging lenses?
A: Converging lenses bring parallel light rays to a focus, while diverging lenses spread them apart. This calculator is for converging lenses only.

Q2: How does focal length affect image formation?
A: Shorter focal lengths produce greater magnification but shorter image distances. Longer focal lengths produce less magnification but longer image distances.

Q3: What are typical focal lengths for common lenses?
A: Eyeglass lenses: 0.1-1m, Camera lenses: 0.01-0.5m, Magnifying glasses: 0.05-0.2m.

Q4: When is the image real vs. virtual?
A: For converging lenses, when do > f, the image is real and inverted. When do < f, the image is virtual and upright.

Q5: Does this work for thick lenses or lens systems?
A: This equation is for ideal thin lenses. Thick lenses and lens systems require more complex calculations.