The object-lens distance for a certain converging lens is 400 mm.The image is three times the size of the object.To make the image five times the size of the object, the object-lens distance must be changed to:
A)360 mm
B)540 mm
C)600 mm
D)720 mm
E)960 mm

Question

Quizplus · Accepted Answer

For a converging lens, the lens formula is 1/f = 1/v - 1/u, where f is the focal length, v is the image distance, and u is the object distance. The magnification (m) is given by -v/u. Initially, m = -3, so -v/u = -3 or v = 3u. To find the focal length, we substitute v = 3u into the lens formula: 1/f = 1/(3u) - 1/u = -2/(3u). For u = 400 mm, we find f. To make the image five times the size of the object, m = -5, so -v/u = -5 or v = 5u. Using the same focal length, we solve for the new u to get the object-lens distance for a 5 times magnification. The calculation shows that the new object-lens distance is 360 mm.

The Object-Lens Distance for a Certain Converging Lens Is 400