A compound lens system consists of two converging lenses, one at x = -20 cm with
ID: 1290445 • Letter: A
Question
A compound lens system consists of two converging lenses, one at x = -20 cm with focal length f1 = +10 cm, and the other at x = +20 cm with focal length f2 = +8.00 cm. An object 11 cm tall is placed at x = -53cm.
(a) What is the location of the final image produced by the compound lens system? Give the x coordinate of the image.
(b) Suggested - Sketch a ray diagram showing how this final image is created. Use at least 2 principle rays for each lens.
(c) How tall is the image?
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 f3 at x = 0. We want to choose this new lens so that it produces an image at the same location as before.
(e) What is the focal length f3 of this new lens?
A compound lens system consists of two converging lenses, one at x = -20 cm with focal length f1 = +10 cm, and the other at x = +20 cm with focal length f2 = +8.00 cm. An object 11 cm tall is placed at x = -53cm. (a) What is the location of the final image produced by the compound lens system? Give the x coordinate of the image. (b) Suggested - Sketch a ray diagram showing how this final image is created. Use at least 2 principle rays for each lens. (c) How tall is the image? 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 f3 at x = 0. We want to choose this new lens so that it produces an image at the same location as before. (e) What is the focal length f3 of this new lens?Explanation / Answer
1)
s1 = 53-20 = 33
s1' =
lens 1
1/s1 + 1/s1' = 1/f
(1/(33) + (1/s1') = 1/10
s1'= 14.37 cm
it is at x = -(20-14.37) = 5.63 cm
m1 = -s1'/s1 = 0.435
for lens 2
s2 = 5.63+20 = 25.63 cm
1/s2 + 1/s2' = 1/f2
s2' = 11.63
the final image i at x = 20 + 11.63 = 31.63 cm
m2 = -s2'/s2 = 0.453
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c) M = y'/y = m1*m2
y' = 2.17 cm
e) 1/s + 1/s' = 1/f
(1/53)+(1/31.63)=(1/f)
f = 19.8 cm
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