Focal Length Calculator
Calculate focal length, object distance, image distance, and magnification using the thin lens equation 1/f = 1/u + 1/v.
Find Focal Length (f)
Find Object Distance (u)
Find Image Distance (v)
Converging (f > 0)
Diverging (f < 0)
cm
mm
m
in
cm
mm
m
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For diverging lens, image distance is negative (virtual image).
Common Lenses
Presets set focal length for reference. Enter other values as needed.
Focal Length (f)
0.00 cm
Formula: 1/f = 1/u + 1/v
Formula Used
1/f = 1/u + 1/v
Magnification (m)
-
Lens Power (diopters)
-
Thin Lens Formulas
1/f = 1/u + 1/v
m = v / u
P = 1 / f (in meters)
f: focal length (positive for converging, negative for diverging)
u: object distance (positive if object is on the side from which light comes)
v: image distance (positive for real image on opposite side, negative for virtual image on same side)
m: magnification (negative means inverted image, positive means upright)
P: lens power in diopters (m⁻¹)
People Also Ask
🤔 What is focal length and how is it measured?
Focal length is the distance from the lens to its focal point. It determines how strongly the lens converges or diverges light. Measured in mm, cm, or meters.
🔍 How to calculate focal length from object and image distances?
Use the thin lens formula: 1/f = 1/u + 1/v. Plug in u and v (with proper signs) and solve for f.
⚡ What is the difference between converging and diverging lenses?
Converging lenses (positive f) focus parallel light to a real focal point. Diverging lenses (negative f) spread light as if coming from a virtual focal point.
📏 How is magnification related to image and object distances?
Magnification m = v/u. A negative m means inverted image; positive m means upright. |m|>1 means enlarged, |m|<1 means reduced.
🎯 What is lens power and its unit?
Lens power P = 1/f (with f in meters). Unit: diopter (D). Converging lens: positive diopters; diverging: negative diopters.
🔥 Real-world applications of focal length calculations?
Camera lenses, eyeglasses, microscopes, telescopes, projectors, and optical design in general.
The Thin Lens Equation
The thin lens equation relates the focal length (f), object distance (u), and image distance (v):
1/f = 1/u + 1/v
Sign conventions vary; we use the Cartesian sign convention: distances are positive if measured in the direction of incident light, negative otherwise. For simplicity, this calculator assumes:
- Object distance u is always positive (real object).
- For converging lenses, f > 0; for diverging, f < 0.
- Image distance v is positive for real images (opposite side), negative for virtual images (same side as object).
Magnification
m = v / u. The image height h' = m × h. Negative m means inverted image.
How to Use This Calculator
Select what you want to find: focal length, object distance, or image distance. Enter the known values, choose units, and click Calculate. The calculator will display the result, magnification, and lens power in diopters.
Note: Ensure you select the correct lens type (converging/diverging) as it affects the sign of focal length. For diverging lenses, enter negative focal length if you know it.
Typical Focal Lengths
| Lens Type | Typical Focal Length | Application |
|---|---|---|
| Eyeglass (hyperopia) | +20 to +40 cm | Correct farsightedness |
| Eyeglass (myopia) | -20 to -40 cm | Correct nearsightedness |
| Magnifying glass | +5 to +15 cm | Reading, inspection |
| Camera lens (standard) | 50 mm (full frame) | General photography |
| Camera lens (telephoto) | 200 mm | Sports, wildlife |
| Microscope objective | 2 to 10 mm | High magnification |
| Telescope objective | 500 to 2000 mm | Astronomy |
Common Questions
How to find focal length if image is at infinity?
When object is at focal point, image is at infinity. Then 1/f = 1/u + 1/∞ = 1/u → f = u. So measure object distance when image appears at infinity (collimated beam). This is how telescopes are focused.
What is the focal length of a flat (plano) lens?
A flat piece of glass has infinite focal length (no focusing power). It doesn't converge or diverge light.