Two converging lenses, the first with focal length 10.0 cm and the second with focal length 20.0 cm, are separated by 40.0 cm. An object, 3.00 cm in height, is placed 30.0 cm in front of the first lens. Where is the image formed by the first lens?
A) 7.50 cm after the first lens
B) 7.50 cm after the second lens
C) 15.0 cm after the first lens
D) 15.0 cm after the second lens
E) 55.0 cm after the second lens

Question

Quizplus · Accepted Answer

Using the lens equation for the first lens, 1/f = 1/do + 1/di, where f = 10.0 cm, do = -30.0 cm (since the object is placed in front of the lens), and di is the distance of the image from the first lens. Solving for di, we get di = 15.0 cm. This image now acts as the object for the second lens. Using the lens equation again for the second lens, 1/f = 1/do + 1/di, where f = 20.0 cm, do = 25.0 cm (since the object distance is now the distance from the first lens to the image formed by it, which is 15.0 + 10.0 = 25.0 cm), and we want to find di, the final image distance. Solving for di, we get di = 55.0 cm. Therefore, the final image is formed 15.0 cm after the first lens, which is choice C.

Two Converging Lenses, the First with Focal Length 10