1. What is the Focal Length Formula?

The focal length formula calculates the focal length of a lens based on the object distance and image distance. It's derived from the thin lens equation and is fundamental in optics.

2. How Does the Calculator Work?

The calculator uses the focal length formula:

Where:

• \( f \) — Focal length (meters)
• \( d_o \) — Object distance (meters)
• \( d_i \) — Image distance (meters)

Explanation: The formula shows the reciprocal relationship between focal length and the sum of reciprocals of object and image distances.

3. Importance of Focal Length Calculation

Details: Calculating focal length is essential for designing optical systems, camera lenses, telescopes, and understanding image formation.

4. Using the Calculator

Tips: Enter both object and image distances in meters. Both values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between f and 1/f?
A: f is the focal length, while 1/f is the optical power of the lens measured in diopters.

Q2: Can this formula be used for thick lenses?
A: This formula is most accurate for thin lenses. For thick lenses, more complex calculations are needed.

Q3: What happens if do equals di?
A: When object distance equals image distance, the focal length will be half of that distance (f = do/2 = di/2).

Q4: How does focal length affect magnification?
A: Magnification (m) is related to focal length by m = di/do = f/(do - f).

Q5: What are typical focal length values?
A: Focal lengths vary widely - from millimeters in camera lenses to meters in astronomical telescopes.