1. What is the Lens Formula?

The lens formula relates the focal length of a lens to the distances of the object and the image from the lens. It is fundamental in optics for determining image formation by lenses.

2. How Does the Calculator Work?

The calculator uses the lens formula and magnification formula:

Where:

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

Explanation: The negative sign in the magnification formula indicates that the image is inverted relative to the object.

3. Importance of Image Distance Calculation

Details: Calculating image distance and magnification helps determine image characteristics (real/virtual, upright/inverted, size) which is crucial in optical system design and analysis.

4. Using the Calculator

Tips: Enter focal length and object distance in meters. Both values must be positive. The calculator will determine image distance and magnification.

5. Frequently Asked Questions (FAQ)

Q1: What does a negative image distance mean?
A: A negative image distance indicates a virtual image formed on the same side as the object.

Q2: What does magnification tell us?
A: Magnification indicates the size ratio of image to object. Absolute value >1 means enlarged, <1 means reduced.

Q3: How does focal length affect the image?
A: Shorter focal lengths produce larger magnifications for a given object distance.

Q4: What's the difference between convex and concave lenses?
A: Convex lenses have positive focal lengths and can form real images. Concave lenses have negative focal lengths and always form virtual images.

Q5: Can this calculator be used for mirrors?
A: Yes, the same formulas apply to spherical mirrors with appropriate sign conventions.