Lens formula
Intermediate
Thin lens equation.
1/v − 1/u = 1/f1/v − 1/u = 1/f in the Cartesian convention (u negative for real objects). Magnification m = v/u.
f = 10 cm, u = −30 cm: v = 15 cm, m = −0.5.
Keep the sign convention consistent.
In more detail
The lens formula 1/v − 1/u = 1/f relates object distance, image distance and focal length for thin lenses, with the sign convention applied consistently.
Real-world uses
- Camera lenses are designed to focus at specified distances.
- Projectors place lenses to form sharp images on screens.
- Opticians use the thin lens equation to find the focal length needed to correct a person's vision.
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Frequently asked questions
What does the sign of v mean?
Positive v means the image is real and on the far side of the lens.
Can the formula find magnification?
Yes, m = v/u, with the sign indicating orientation.
Does the sign of u matter?
Yes. In the usual convention, object distances are taken as negative for real objects, so check the sign carefully.
Related topics in Optics
Mirage · Refraction at a spherical surface · Thin lens · Lens maker's formula · Power of a lens · Combination of lenses