When two lenses are used in combination, the first one forms an image that then

Question

When two lenses are used in combination, the first one forms an image that then serves as the object for the second lens. The magnification of the combination is the ratio of the height of the final image to the height of the object. A 1.20 cm -tall object is 50.0 cm to the left of a lens of focal length of magnitude 40.0 cm . A second lens, this one having a focal length of magnitude 60.0 cm , is located 300 cm to the right of the first lens along the same optic axis.

E. Find the location and height of the image (call it I3) formed by the lens with a focal length of 40.0 cm if both lenses are diverging lenses.

F. I3 is now the object for the second lens. Find the location and height of the image produced by the second lens.

Explanation / Answer

u = -50 cm
h = 1.2 cm
f = -40cm
f' = 60cm
d = 300cm
E. for lens 1:

1/v - 1/u = 1/f
1/v + 1/50 = -1/40
v = -22.22 cm
m = v/u = h'/h
h' = 22.22*1.2/50 = 0.53328 cm

F. for lens 2, -u = d - v = 322.22 cm
v = ?
f = -60cm
1/v - 1/u = 1/f
v = -50.581 cm
m = v/u = h'/h
h' = 50.581*0.53328/322.22 = 0.083712 cm

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