Two convex thin lenses with focal lengths 10.0 cm and 20.0 cm are aligned on a common axis,running left to right,the 10-cm lens being on the left.A distance of 20.0 cm separates the lenses.An object is located at a distance of 15.0 cm to the left of the 10-cm lens.Where will the final image appear as measured from the 20-cm lens?

Question

Quizplus · Accepted Answer

Using the lens formula, 1/f = 1/u + 1/v, where f is the focal length of the lens, u is the object distance, and v is the image distance:

For the first lens, with f=10 cm:
1/10 = 1/15 + 1/v1
v1 = 30 cm

The image produced by the first lens acts as the object for the second lens. So the object distance for the second lens is u2 = 20 - 30 = -10 cm (negative because the object is to the left of the lens).

For the second lens, with f=20 cm:
1/20 = 1/-10 + 1/v2
v2 = -6.67 cm (negative because the image is formed to the left of the lens)

The final image is formed 6.67 cm to the right of the second lens (as measured from the 20-cm lens). Therefore, the answer is C.

Two Convex Thin Lenses with Focal Lengths 10