Lens Formula Calculator
Calculate focal length, image distance, or object distance using the lens formula 1/f = 1/v - 1/u
Find Focal Length (f)
Find Image Distance (v)
Find Object Distance (u)
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⚠️ Use Cartesian sign convention:
• u is negative for real object (left of lens)
• v positive for real image (right of lens), negative for virtual
• f positive for converging lens, negative for diverging
• u is negative for real object (left of lens)
• v positive for real image (right of lens), negative for virtual
• f positive for converging lens, negative for diverging
Common Examples
Focal Length
10.00 cm
Magnification (m)
-
Image Height
-
Image Orientation
-
Lens Type
Converging
Formula Used
1/f = 1/v - 1/u
Sign Convention
Cartesian
Lens Formula & Magnification
1/f = 1/v – 1/u
f = focal length (positive for converging, negative for diverging)
v = image distance (positive for real image, negative for virtual)
u = object distance (negative when object is on the side from which light comes)
Magnification m = v / u (negative = inverted, positive = upright)
Image height hi = m × ho
People Also Ask
🔍 What is the Cartesian sign convention for lenses?
Object distance (u) is negative if object is on the incident side. Image distance (v) positive for real image, negative for virtual. Focal length positive for converging lenses.
📏 How do I calculate magnification from lens formula?
Magnification m = v / u. Negative m means inverted image; positive means upright. Also m = hᵢ / hₒ.
🔄 What's the difference between converging and diverging lenses?
Converging (positive f) focus parallel light to a real focus. Diverging (negative f) spread light, appearing to come from a virtual focus.
📸 How do I use the lens formula for camera lenses?
Camera lenses are converging. For an object at distance u, image distance v adjusts to focus on sensor. Formula helps compute required v.
Understanding the Lens Formula
The lens formula relates the focal length (f), object distance (u), and image distance (v) for thin lenses. It is derived from geometry and the paraxial approximation. The formula works for both converging and diverging lenses when the correct sign convention is used.
Sign Convention (Cartesian)
- Object distance u is negative if the object is on the side from which light comes (real object).
- Image distance v is positive if the image is formed on the opposite side (real image), negative if on the same side (virtual image).
- Focal length f is positive for converging (convex) lenses, negative for diverging (concave) lenses.
Magnification tells you how much larger or smaller the image is compared to the object, and whether it's upright or inverted.
Typical Lens Scenarios
| Lens Type | Object Position | Image Position | Image Nature | Magnification |
|---|---|---|---|---|
| Converging (convex) | u > 2f | f < v < 2f | Real, inverted, reduced | |m| < 1 |
| Converging | u = 2f | v = 2f | Real, inverted, same size | |m| = 1 |
| Converging | f < u < 2f | v > 2f | Real, inverted, enlarged | |m| > 1 |
| Converging | u < f | v negative (same side) | Virtual, upright, enlarged | m > 1 |
| Diverging (concave) | Any u | v negative (same side) | Virtual, upright, reduced | |m| < 1 |
Frequently Asked Questions
What happens if I get a negative focal length?
Negative focal length indicates a diverging lens. Light rays diverge after passing through, and the focus is virtual (on the same side as the object).
Why is object distance usually negative in calculations?
In Cartesian convention, distances measured opposite to the direction of incident light are negative. Since light travels from object to lens, the object distance is taken as negative.
Can the lens formula be used for thick lenses?
The thin lens formula is an approximation. For thick lenses, more complex formulas (like lensmaker's equation) or ray tracing are required.