Two-lens systems. In the figure, stick figure O (the object) stands on the commo

Question

Two-lens systems. In the figure, stick figure O (the object) stands on the common central axis of two thin, symmetric lenses, which are mounted in the boxed regions. Lens 1 is mounted within the boxed region closer to O, which is at object distance p_1. Lens 2 is mounted within the farther boxed region, at distance d. Each problem in the table refers to a different combination of lenses and different values for distances, which are given in centimeters. The type of lens is indicated by C for converging and D for diverging; the number after C or D is the distance between a lens and either of its focal points (the proper sign of the focal distance is not indicated). Find (a) the image distance i2 for the image produced by lens 2 (the final image produced by the system) and (b) the overall lateral magnification M for the system, including signs. Also, determine whether the final image is (c) real or virtual, (d) inverted from object O or noninverted, and (e) on the same side of lens 2 as object O or on the opposite side.

Explanation / Answer

find the image formed by first lens this image will work like object for second lens

formula

1/v -1/u = 1/ f

1/ v - 1/ -12 = 1/ 8.1

v = 24.9231

m = v/ u = 24.9231/ -12 = -2.076925

distance of this image from second lens

38 -  24.9231 =13.0769 cm

now same formual for final image

1/ v-1/u = 1/ f

1/ v - 1/ -13.0769 = 1/ -9.3

v = -5.4348 cm in left of the second lens

m = v/ u =  -5.4348 / -13.0769 =0.4156

total magnitude =   -2.076925 * 0.4156 = -0.863

final image wil be

inverted virtual samll & left side of the second lens distance = 5.348 cm from lens 2

and ( 38 - 5.348) =32.652 from lens 1

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