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 1.70 cm-tall object is 60.0 cm to the left of a converging lens of focal length 40.0 cm. A second converging lens, this one having a focal length of 60.0cm, is located 300 cm to the right of the first lens along the same optic axis.

Find the location and height of the image (call it I1) formed by the lens with a focal length of 40cm

s1,y1' =

I1 is now the object for the second lens. Find the location and height of the image produced by the second lens. This is the final image produced by the combination of lenses.

s'2, y2'=

Please help! Thank you!

Explanation / Answer

For the first lens

1/f = 1/p + 1/q

1/40 = 1/60 + 1/q

q = 120 cm, so s1 = 120 cm

For the height h'/h = -q/p

h'/1.7 = -(120)/60

h' = -3.40 cm (The negative means its inverted, ignore it if necessary)

For the second lens, the image is 300 - 120 = 180 cm away since the lenses are 300 cm apart

1/60 = 1/180 + 1/q

q = 90 cm

So s2 is 90.0 cm

For this height,

h'/-3.4 = -90/180

h' = 1.70 cm tall (back to its initial height)

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