Lens Calculator
Calculate focal length, image distance, or magnification with the thin lens equation.
Result
Magnification (m)
Calculation Details
The Thin Lens Equation
The thin lens equation relates the focal length of a lens to the object and image distances measured along the optical axis. For an ideal thin lens, the equation 1/f = 1/do + 1/di holds, where f is the focal length, do is the distance from the object to the lens, and di is the distance from the lens to the image. Knowing any two of these quantities lets you solve for the third.
Key Formulas
- 1/f = 1/do + 1/di — The thin lens equation
- f = 1 / (1/do + 1/di) — Solve for focal length
- di = 1 / (1/f − 1/do) — Solve for image distance
- do = 1 / (1/f − 1/di) — Solve for object distance
- m = −di / do — Magnification of the image
Lenses and Sign Conventions
Converging Lens
- • Positive focal length (f > 0)
- • Thicker at the center than at the edges
- • Can form real, inverted images
- • Used in cameras, magnifiers, and the eye
Diverging Lens
- • Negative focal length (f < 0)
- • Thinner at the center than at the edges
- • Always forms virtual, upright images
- • Used to correct nearsightedness
Image Distance (di)
- • Positive for real images (opposite side)
- • Negative for virtual images (same side)
- • Measured along the optical axis
- • Determines where the image forms
Magnification (m)
- • Formula: m = −di / do
- • |m| > 1 means the image is enlarged
- • Negative m indicates an inverted image
- • Positive m indicates an upright image
Real-World Examples
The thin lens equation is fundamental to optics, photography, and vision science. Here are some practical applications:
- An object 30 cm from a lens forming an image 15 cm away has a focal length of 10 cm
- A camera lens focuses light from a distant scene onto the sensor at its focal plane
- A magnifying glass placed within its focal length produces an enlarged, upright virtual image
- Eyeglasses use converging or diverging lenses to shift the focal point onto the retina
References
The formulas used in this calculator are based on established optics principles and verified sources:
Related Calculators
Note: This calculator uses the ideal thin lens approximation and the Cartesian sign convention (1/f = 1/do + 1/di). It does not account for lens thickness, aberrations, or dispersion. Results are intended for educational purposes and may differ from real optical systems.