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 convex lens is placed 7.29 m behind the first lens with a focal length 4.3 m (sec 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

For convex lens 1 :

f = 5.2 m

do = object distance = 10 m

di = image distance

using the lens equation

1/di + 1/do = 1/f

1/di + 1/10 = 1/5.2

di = 10.83 m

2)

m1 = - di/do = - 10.83 / 10 = - 1.083

3)

for second lens

f = 4.3 m

do = object distance = 7.29 - 10.83 = 3.54

di = image distance

using the lens equation

1/di + 1/do = 1/f

1/di + 1/3.54 = 1/4.3

di = - 20.03 m

distance = 20.03

4)

m2 = - di/do = - (-20.03) / 3.54 = 5.66

final image magnification = m1 m2 = (- 1.083 ) (5.66)= - 6.13

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