A compound lens system consists of two converging lenses, one at x = -20.0 cm wi

Question

A compound lens system consists of two converging lenses, one at x = -20.0 cm with focal length f_1 = +10.0 cm, and the other at x = +20.0 cm with focal length f_2 = +8.00 cm. (Figure 1^An object 1.00 centimeter tall is placed at x = -50.0 cm. What is the location of the final image produced by the compound lens system? Give the x coordinate of the image. Express your answer in centimeters, to three significant figures or as a fraction. This question will be shown after you complete previous question(s). This question will be shown after you complete previous question(s). Now remove the two lenses at x = +20.0 cm and x = -20.0 cm and replace them with a single lens of focal length f_at x = 0. We want to choose this new lens so that it produces an image at the same location as before. What is the focal length of the new lens at the origin? Express your answer in centimeters, to three significant figures or as a fraction.

Explanation / Answer

Part A,
f1 = 10.0 cm
f2 = 8.0 cm
Distance of object from 1st lens, do = 30 cm

we know,
1/f1 = 1/do + 1/di
1/10 = 1/30 + 1/di
di = 15 cm

Now this image from 1st lens acts as an object for the second lens.
So, DIstance of object from 2nd lens, = 40 - 15 = 25 cm

Again,
1/f2 = 1/di + 1/do
1/8 = 1/di + 1/25
di = 11.76 cm

Location of final image, = 20 + 11.76
Location of final image, = 31.76 cm

Part D)
Let the Focal length of the new lens be f3

do = 50 cm
di = 31.76 cm

We know,
1/f3 = 1/di + 1/do
1/f3 = 1/31.76 + 1/50
f3 = 19.42 cm
Focal length of the new lens, f3 = 19.42 cm

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