The thin lens equation relates object distance, image distance, and focal length. Which form is correct?

• A. o = f + i
• B. 1/f = 1/o + 1/i
• C. f = o + i
• D. 1/o = 1/f + 1/i

Answer: (B)

The relationship among object distance, image distance, and focal length for a thin lens is given by the reciprocal sum 1/f = 1/o + 1/i. This comes from the geometry of how rays bend through a thin lens under the thin-lens approximation and is consistent when you apply a clear sign convention: o is positive for an object in front of the lens, i is positive for a real image on the opposite side, and f is positive for a converging lens. When the image is virtual, i becomes negative, but the same equation with signed distances still holds. The other forms either imply distances add directly or present a different reciprocal relationship, which does not match the geometric derivation of how lenses form images.