A thin lens with focal length f = 10 cm forms an image when the object is at do = 15 cm. What is the image distance di?

• A. 15 cm
• B. 30 cm
• C. -30 cm
• D. 5 cm

Answer: (D)

The key relationship here is the thin lens equation, which connects the focal length, the distance from the object to the lens, and the distance from the lens to the image: 1/f = 1/do + 1/di. For a converging lens, both f and do are taken as positive, and a real image appears on the opposite side of the lens, giving a positive di.

Plug in f = 10 cm and do = 15 cm. Solve for di: 1/di = 1/f − 1/do = 1/10 − 1/15 = 1/30, so di = 30 cm. Since di is positive, the image is real and forms 30 cm to the other side of the lens. The magnification is m = −di/do = −30/15 = −2, meaning the image is inverted and twice as large as the object. Therefore, the image distance is 30 cm.