Which equation correctly represents the thin lens equation relating object distance do, image distance di, and focal length f?

• A. f = d_o + d_i
• B. f = d_i - d_o
• C. 1/f = 1/d_o + 1/d_i
• D. m = - di/do

Answer: (C)

The distance relationships for a thin lens come from how light rays pass through the lens and converge or diverge, which leads to a neat reciprocal-distance form. In the thin-lens setup, using geometry of similar triangles in the paraxial (small-angle) approximation gives 1/f = 1/d_o + 1/d_i, where f is the focal length and d_o and d_i are the object and image distances measured from the lens. This arrangement matches the way the lens anchors the convergence: if the object is very far away, d_o is large and 1/d_o is near zero, so the image sits at the focal distance f; if the image is very far away, d_i is large and 1/d_i is near zero, so the object distance approaches f. Among the common ways to express the relationships, this reciprocal-sum form is the one that ties together the three quantities in a way that reflects the lens’s bending of light. The other forms either imply a simple sum, a difference, or describe a different aspect of imaging; for example, m = - d_i/d_o gives how large the image is relative to the object, not how the focal length relates to the distances.