Three-lens systems. In the figure below, stick figure O (the object) stands on t

Question

Three-lens systems. In the figure below, stick figure O (the object) stands on the common central axis of three thin, symmetric lenses. Lens 1 is mounted within the boxed region closest to O, which is at object distance p1. Lens 2 is mounted within the middle boxed region, at distance d12 from lens 1. Lens 3 is mounted within the farther boxed region, at distance d23 from lens 2.

The table refers to the type of lens (C for converging, D for diverging), focal distances f1,  f2, and f3 for lens 1, lens 2 and lens 3 respectively, the image distance i3 for the final image produced by lens 3 (the final image produced by the system) and the overall lateral magnification m for the system. All distances are in centimeters. Fill in the missing information, including signs.

* indicates a sign was not given

What is i3 and m?

Describe the image (select all that apply)

real / virtual ?

upright / inverted ?

on the same side of lens 3 as object O / on the opposite side ?

P1 Lens 1 f1 d12 Lens 2 f2 d23 Lens 3 f3 i3 m +12 C *8.4 28 C *6 8.0 C *4.5 ----- -----

Explanation / Answer

for lens system 1

objec distance p1 = 12

image distance q1 = ?

focal length f1 = +8.4

from lens equation

1/p1 + 1/q1 = 1/f1

1/12 + 1/q1 = 1/8.4

q1 = (8.4*12)/(12-8.4) = 28 cm

m1 = p1/q1 = 28/12 = 2.33

-----

for 2

p2 = 0

f2 = +6

1/p2 + 1/q2 = 1/f2

q2 = (p2*f2)/(p2-f2) = 0

for 3

p3 = d23 = 8

f3 = +4.5

1/p3 + 1/q3 = 1/f3

1/8 + 1/q3 = 1/4.5

q3 = +10.3 cm

i3 = +10.3 cm

m3 = i3/p3 = 1.3 cm <<<----answer

real <<<----answer

on the opposite side   <<<----answer

m = m1*m3 = 3.03 <<<----answer

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