Lens & Mirror Formula Calculator Physics

Image: --
Results:
Enter values and click Calculate.

What is the Lens & Mirror Formula Calculator?

Quick Answer: An interactive tool that computes image distance (v) and magnification (m) using the mirror/lens formula. Simply input object distance (u) and focal length (f) with proper sign convention, and instantly get the image position and nature. A basic ray diagram shows object and image placements.

Theory of the Mirror and Lens Equations

The mirror formula is 1/f = 1/v + 1/u and the lens formula is 1/f = 1/v - 1/u (using Cartesian sign convention where object distance u is negative for real objects). Magnification is m = -v/u for mirrors and m = v/u for lenses. Positive m indicates an upright image; negative m indicates an inverted image. The sign of v tells if the image is real (positive for mirrors, negative for lenses? Wait: in Cartesian convention, for mirrors, v is negative if image is real (in front of mirror); for lenses, v is positive if image is real (on opposite side). The tool uses standard physics sign conventions and explains the image characteristics accordingly.

Step-by-Step Examples

Example 1: Concave Mirror

  1. Select Mirror > Concave. Enter u = -20 cm, f = -10 cm (f is negative for concave mirror). Click Calculate.
  2. Image distance v = -6.67 cm (real, inverted, between F and C). Magnification m = -0.33 (diminished).
  3. Observe the ray diagram: the image is formed on the same side as the object.

Example 2: Convex Lens

  1. Select Lens > Convex. Enter u = -20 cm, f = +10 cm (f positive for convex lens).
  2. v = +20 cm (real, on opposite side). m = -1 (same size, inverted).

Example 3: Sign Convention Exploration

  1. Try concave lens (f negative, u negative) to see virtual image formation.

Frequently Asked Questions

What sign convention is used?

Cartesian sign convention: Light travels left to right. Object distance u is negative for real objects. Focal length f is negative for concave mirrors and positive for convex lenses, etc. The tool applies this automatically based on your selections.

How do I know if the image is real or virtual?

For mirrors, if image distance v is negative, the image is real (in front of the mirror). For lenses, if v is positive, the image is real (on the opposite side of the lens). The result panel describes it.

Can I enter distances without signs?

You must enter u and f with signs according to the Cartesian convention. The default values show correct signs for a typical concave mirror. Check the theory for guidance.

Why does the ray diagram look basic?

The diagram shows the principal axis and approximate positions of object and image to scale. It's a quick visual aid, not a full ray tracing simulation.

Does this cover the lens maker formula?

No, this calculator specifically uses the mirror and lens equations for image formation. A separate lens maker's formula tool is planned.