Two converging lenses, the first with focal length 10.0 cm and the second with f

Question

Two converging lenses, the first with focal length 10.0 cm and the second with focal length 20.0 cm, are separated by 40.0 cm. An object, 3.00 cm in height, is placed 30.0 cm in front of the first lens. Where is the final image formed?

11.1 cm after the second lens
100 cm after the second lens
45.0 cm after the second lens
5.00 cm after the second lens
5.00 cm before the second lens

Just thinking about it it makes sense to me that it should be formed after but I don't know how to equate the distance. Please help!

Explanation / Answer

Apply the lens equation for the first lens

1/f = 1/p + 1/q

1/10 = 1/30 + 1/q

q = 15 cm

This means the first lens forms an image 15 cm behind it. Since the second lens is 40 cm away, this image is 40 - 15 = 25 cm in front of the second lens and it becomes the object for the second lens. Thus apply the lens equation again

1/f = 1/p + 1/q

1/20 = 1/25 + 1/q

q = 100 cm

This means that the final image is 100 cm behind the second lens which is the first choice of the multiple choice answers.

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