Thin Lens & Mirror
Image distance, magnification, and ray diagram
About this calculator
The Thin Lens & Mirror Calculator solves the equation 1/f = 1/dₒ + 1/dᵢ under the standard real-is-positive sign convention, giving the image distance, magnification m = −dᵢ/dₒ, and optionally the image height. It classifies the image as real or virtual, upright or inverted, and enlarged or reduced, tells you whether the element is converging or diverging, and reports the special case where an object at the focal point sends the image to infinity.
How to use the Thin Lens & Mirror calculator
- Enter the quantities you know, using the units shown on each field.
- Read the computed results — they update instantly as you type.
- Use the visual explanation to see how the quantities relate.
- Copy the page URL to share the exact calculation.
Common examples
- Converging lens f = 10 cm, object at 30 cm → image at 15 cm, m = −0.5: real, inverted, half size
- Object inside the focal length (f = 10 cm, dₒ = 5 cm) → dᵢ = −10 cm, m = 2: virtual, upright, enlarged (a magnifying glass)
- Diverging lens f = −10 cm, object at 20 cm → dᵢ ≈ −6.67 cm: virtual, upright, reduced
- Concave mirror f = 15 cm, object at 30 cm → image at 30 cm, m = −1: real, inverted, same size
- Object at the focal point (dₒ = f = 10 cm) → rays exit parallel, image at infinity
Frequently asked questions
How does the Thin Lens & Mirror calculator work?
Enter the known quantities and the calculator applies the governing physical law or scientific formula to find the unknowns, stating the equation it used and the units of every result. Computations run at high precision.
When would I use the Thin Lens & Mirror calculator?
It suits physics and chemistry homework, lab work, engineering estimates, and any time you want to explore how changing one quantity affects the others in a well-defined scientific relationship.
How accurate are the results?
The formula itself is evaluated at 30 significant digits of precision. Keep in mind that idealized models — such as neglecting friction, air resistance or measurement error — bound the real-world accuracy more than the arithmetic does.
Can I share a specific calculation with someone else?
Yes. Every value you enter updates the URL, so copying the address bar and sharing the link reopens the exact same calculation for whoever clicks it.