An object is placed 10 m before a convex lens with focal length 5.2 m. Another c

Question

An object is placed 10 m before a convex lens with focal length 5.2 m. Another concave lens is placed 8.32 m behind the first lens with a focal length -4.6 m (see the figure below). Note: Make a ray diagram sketch in order to check your numerical answer. At what distance is the first image from the first lens? Answer in units of m. What is the magnification of the first image? At what distance is the second image from the second lens? Answer in units of m. What is the magnification of the final image, when compared to the initial object?

Explanation / Answer

do = 10 m
f = 5.2 m

For convex lens,
1/f = 1/di + 1/do
1/5.2 = 1/di + 1/10
di = 10.83 m
Distance of image from the 1st lens, di =  10.83 m

M = - di/do
M = - 10.83/10.0
M = - 1.08
Magnification of the first lens, M = - 1.08

Now Distance of object for the second lens, do = 8.32 - 10.83 = -2.51 m
f = -4.6 m

1/f = 1/di + 1/do
-1/4.6 = 1/di - 1/2.51
di = 5.52 m
Distance of image from the 2nd lens, di =  5.52 m

M2 = -di/do = -5.52/2.51 = - 2.2

Total Magnification = M1 * M2
Total Magnification = 1.08 * 2.2
Total Magnification = 2.376

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