1. What is the Image Distance Formula?

The image distance formula calculates the distance between the lens and the formed image based on the focal length of the lens and the magnification of the system. It's fundamental in optics and lens design.

2. How Does the Calculator Work?

The calculator uses the image distance formula:

Where:

• \( d_i \) — Image distance (meters)
• \( f \) — Focal length of the lens (meters)
• \( m \) — Magnification (dimensionless)

Explanation: The formula relates the position of the image to the lens's focal length and the magnification of the optical system.

3. Importance of Image Distance Calculation

Details: Calculating image distance is essential for designing optical systems, camera setups, and understanding how lenses form images in various applications.

4. Using the Calculator

Tips: Enter focal length in meters and magnification (positive for upright images, negative for inverted). Magnification cannot be exactly 1 (would cause division by zero).

5. Frequently Asked Questions (FAQ)

Q1: What does negative image distance mean?
A: Negative values indicate virtual images formed on the same side as the object.

Q2: How does magnification affect image distance?
A: As magnification approaches 1, image distance increases dramatically. At m=1, the formula is undefined.

Q3: What are typical values for focal length?
A: Camera lenses range from wide-angle (short f) to telephoto (long f). Common values are 0.05m to 0.5m.

Q4: Can this be used for concave lenses?
A: Yes, but remember focal length is negative for diverging lenses.

Q5: How does this relate to the thin lens equation?
A: This formula is derived from the thin lens equation (1/f = 1/d_o + 1/d_i) combined with m = -d_i/d_o.