How to use the Optics Calculator
- Choose a Calculation mode: Lens/mirror image distance, magnification & focal length, Optical power ↔ focal length, or Wavelength ↔ frequency.
- Select the value to calculate in that mode's Solve for control. The selected field is hidden automatically.
- Enter the other visible known values and choose their units.
- Select Calculate to view the result, formula steps, and warnings. Use Reset to clear the inputs.
- Use Copy result or Download result (.txt) to save the result and steps as text.
Lens/mirror image distance, magnification & focal length
Choose Lens or Mirror in Device, then choose Converging (convex lens / concave mirror) or Diverging (concave lens / convex mirror) in Type. The mode uses 1/f = 1/d₀ + 1/dᵢ and m = −dᵢ/d₀ to solve for image distance, object distance, or focal length. Use meters (m), centimeters (cm), millimeters (mm), inches (in), or feet (ft). Enter Object height (h₀, optional) if you also want the image height.
The result includes image type, orientation, size relationship, sign convention, calculation steps, and a ray-diagram-style text summary.
Optical power ↔ focal length
Use Optical power (P) from focal length or Focal length (f) from optical power. The relationship is P = 1/f, with focal length in meters and power in diopters. Supported focal-length units are m, cm, mm, in, and ft. Focal length and optical power cannot be zero.
Wavelength ↔ frequency
Choose Frequency from wavelength, Wavelength from frequency, or Wave speed from wavelength & frequency. The mode uses v = λ × f. Vacuum / air (n ≈ 1) uses c = 299,792,458 m/s; Custom refractive index uses v = c/n.
Wavelength units are nm, µm, mm, and m. Frequency units are Hz, kHz, MHz, GHz, and THz. In speed mode, the result reports an implied refractive index and warns if the calculated speed exceeds c.
Sign convention and input checks
The calculator uses the real-is-positive convention:
- Object distance (d₀) is positive for a real object in front of the device.
- Focal length (f) is positive for a converging device and negative for a diverging device.
- Image distance (dᵢ) is positive for a real image and negative for a virtual image.
- Positive Magnification (m) means upright; negative means inverted.
Required visible numeric inputs must be finite and valid. Object height (h₀, optional) may be blank, and the field selected in Solve for is hidden or omitted. Object distance must be positive; focal length, optical power, wavelength, and frequency cannot be zero where applicable. Warnings cover focal-point geometry, sign mismatches, extreme values, and calculated wave speed above c.
What the calculator assumes
The tool models an ideal thin lens or single spherical mirror with the paraxial approximation, plus basic wavelength-frequency relationships in one non-dispersive medium described by a refractive index. It does not model lens thickness, non-paraxial mirror curvature, multiple optical elements, dispersion, spherical aberration, or chromatic aberration. It does not provide laboratory, prescription, or medical-device guidance.
Calculation data and site privacy scope
Calculations run in the browser, and the calculator workflow does not submit entered calculation values as part of the calculation. This page also includes site analytics and a subscription form, so this statement does not cover all site-wide data handling.
Frequently Asked Questions
What sign convention does this optics calculator use?
It uses the common real-is-positive convention: distances are measured from the lens or mirror, object distance (d₀) is positive for a real object in front of the device, focal length (f) is positive for a converging device (convex lens or concave mirror) and negative for a diverging device (concave lens or convex mirror), image distance (dᵢ) is positive for a real image and negative for a virtual image, and magnification (m) is positive for an upright image and negative for an inverted image.
What is the thin-lens/mirror equation?
1/f = 1/d₀ + 1/dᵢ, where f is focal length, d₀ is object distance, and dᵢ is image distance. The same equation applies to thin lenses and spherical mirrors under this sign convention; magnification is m = −dᵢ/d₀.
How is optical power related to focal length?
Optical power P equals 1 divided by focal length f, with f measured in meters and P reported in diopters (D = 1/m). A converging lens has positive power; a diverging lens has negative power.
How does this calculator relate wavelength and frequency?
It uses v = λ × f, where v is wave speed, λ is wavelength, and f is frequency. In vacuum, v equals the speed of light c (299,792,458 m/s); you can optionally enter a refractive index n to compute the speed and wavelength inside a medium, using v = c / n.
Does this calculator design optical systems or model lens aberrations?
No. It solves the ideal thin-lens/mirror equation and basic wavelength-frequency relationships only. It does not design multi-element optical systems, model spherical or chromatic aberration, or provide laboratory, medical-device, or prescription guidance.