Optics Calculator

1. Choose a mode in Calculation mode: Lens/mirror image distance, magnification & focal length, Optical power ↔ focal length, or Wavelength ↔ frequency.
2. Select the unknown in that mode's Solve for control. The matching input field is hidden.
3. Enter the visible values and choose the unit for each one.
4. Choose Calculate to show the result, steps, and warnings.
5. Choose Copy result or Download result (.txt) to keep the calculation, or choose Reset to clear the form.

How to calculate lens or mirror image distance

Set Device to Lens or Mirror, then choose Type: Converging (convex lens / concave mirror) or Diverging (concave lens / convex mirror). In Solve for, choose Image distance (dᵢ), Object distance (d₀), or Focal length (f). The calculator uses 1/f = 1/d₀ + 1/dᵢ and m = −dᵢ/d₀.

Select a unit in Distance unit. Enter Object height (h₀, optional) when image height is needed.

Device: Lens
Object distance (d₀): 20 cm
Focal length (f): 10 cm
Image distance (dᵢ): 20 cm
Magnification (m): −1

Under the displayed sign convention, d₀ is positive for a real object, f is positive for a converging device, dᵢ is positive for a real image, and positive m means upright. The result also states image type, orientation, size relationship, and a ray-diagram-style description.

How to calculate optical power

Choose Optical power (P) from focal length or Focal length (f) from optical power in Solve for. Enter the remaining value, select a Focal length unit, and use P = 1/f after conversion to meters. The result gives power in diopters (D) and the converted focal length.

Focal length (f): 25 cm
Optical power (P): 4 D

Focal length and optical power must be nonzero. A positive value represents a converging lens; a negative value represents a diverging lens.

How to calculate wavelength or frequency

Choose Frequency from wavelength, Wavelength from frequency, or Wave speed from wavelength & frequency in Solve for. Medium starts at Vacuum / air (n ≈ 1). Choose Custom refractive index to reveal Refractive index (n); the calculator then uses v = c/n. The relationship is v = λ × f.

Choose units in Wavelength unit and Frequency unit. With 500 nm in Vacuum / air (n ≈ 1), the frequency is about 599.585 THz.

What input checks and assumptions does it use?

Numeric inputs must be finite and have an absolute value no greater than 1e12. Values below 1e-9 in absolute value count as zero where zero is rejected. Object distance must be greater than zero; wavelength, frequency, refractive index, focal length, and optical power have their own checks.

Image mode warns about focal-point geometry, sign mismatches, and very large distances. It uses an ideal thin lens or single spherical mirror with a paraxial approximation. The calculator does not model lens thickness, multiple elements, dispersion, or aberrations. Wave speed mode warns when the calculated speed exceeds c.

Examples of calculations

For a convex lens, enter an object distance and focal length, then inspect image distance and magnification in the result. Choose Mirror to solve for focal length from object and image distances.

For a wave calculation, enter a wavelength in nm and choose a frequency unit such as THz. A custom refractive index changes the speed used in the wavelength-frequency calculation.

When another science calculator fits better

Use the Science Calculators category for work outside optics. The Wavelength Calculator covers the general wave equation with any two values. Choose the Physics Calculator for mechanics, energy, electrical, wave, or decay calculations.

Frequently asked questions