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What is an Optics Calculator?

Kalkulab's Optics Calculator is a physics tool designed for calculating various geometric optics parameters, including image distance, focal length, image magnification, and lens power (diopters). This calculator uses the main optics formula 1/f = 1/s + 1/s' (mirror/thin lens formula) and the magnification formula M = |s'/s|. This tool is essential for 12th grade high school students studying the optics chapter in the physics curriculum, physics or engineering students who need quick optical calculations, and physics teachers as an interactive learning medium. With this calculator, complicated optics calculations become very simple and fast.

Geometric Optics Formula

1/f = 1/s + 1/s' | M = |s'/s| | P = 1/f (diopters)

Variables:

  • fFocal Length
    Focal point of mirror/lens from optical center(e.g.: 10 cm (converging))
    💡 Determining eyeglass lens power
  • sObject Distance
    Distance of real object from mirror/lens(e.g.: 15 cm)
    💡 Camera photography, object setup
  • s'Image Distance
    Distance of the formed image(e.g.: 30 cm (real/positive))
    💡 Determining film position in a camera
  • MMagnification
    Ratio of image height to object height(e.g.: 2× (enlarged))
    💡 Designing magnifying glass, microscope, telescope
  • PLens Power
    Refractive power in Diopters (D)(e.g.: -5 D (myopic eye))
    💡 Eyeglass prescription, contact lenses
  • h, h'Object & Image Height
    Vertical dimensions of object and image(e.g.: h=2 cm, h'=4 cm)
    💡 Film projector magnification

Categories:

Convex Lens (f > 0)Converging (+, real focus)
Concave Lens (f < 0)Diverging (-, virtual focus)
M > 1Enlarged image
M < 1Reduced image

How to Use the KalkuLab Optics Calculator

The Optics Calculator has 4 calculation modes. Follow this guide:

  1. 1

    Select Calculator Type

    Choose Mirror & Lens (image formation), Focal Length (find f), Lens Power (diopters), or Magnification (M and image height).

  2. 2

    Select Mirror/Lens Type

    Choose concave mirror (+f), convex mirror (-f), convex lens (converging), or concave lens (diverging).

  3. 3

    Enter Known Values

    Input object distance (s), focal length (f), or image distance (s'). For magnification, also enter object height (h).

  4. 4

    Calculate

    Press Calculate to get image distance, magnification, and image properties.

  5. 5

    Interpret Results

    Check if the image is real or virtual, upright or inverted, and magnified or reduced.

💡 Tip:

  • •Mirror/lens equation: 1/f = 1/s + 1/s'
  • •Magnification: M = -s'/s = h'/h
  • •Sign convention: real is positive for s and s' in most cases
  • •Power in diopters: P = 1/f (f in meters)
  • •Concave mirror and convex lens converge light

Examples

Example 1: Concave Mirror

Problem:

Object 30 cm from a concave mirror with f = 10 cm. Find image distance.

Solution:
  1. 1.1/10 = 1/30 + 1/s'
  2. 2.1/s' = 1/10 - 1/30 = 2/30
  3. 3.s' = 15 cm
Result:s' = 15 cm (real, inverted)

Real inverted image forms 15 cm in front of the mirror.

Example 2: Lens Magnification

Problem:

Object 20 cm from a lens, image at 40 cm. Find M.

Solution:
  1. 1.M = -s'/s = -40/20 = -2
Result:M = -2

Image is 2× enlarged and inverted.

Frequently Asked Questions

What is the mirror equation?
1/f = 1/s + 1/s' relates focal length f, object distance s, and image distance s'. It applies to both mirrors and thin lenses.
What is magnification?
M = -s'/s = h'/h. |M| > 1 means enlarged; |M| < 1 means reduced. Negative M means inverted image.
What are diopters?
Lens power P = 1/f (meters). +2 D means f = 0.5 m converging lens. Used in eyeglass prescriptions.
Is the KalkuLab Optics Calculator free?
Yes, free on KalkuLab anytime.

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References