# Optics - Several lenses

## Homework Statement

1)
I have five lenses with f=25 placed at distance 50 from each other, what is the focal length of this system?
2)
A light source is placed in the focal point of a lens with f=50, at d=600 a lens with f=400 is placed, at the focal point of the second lens the image is captured, what is the magnification?

## Homework Equations

$\frac{1}{A}$+$\frac{1}{B}$ = $\frac{1}{F}$ is everything, I think...

## The Attempt at a Solution

1) I think the light rays will converge 25 after the last lens because for lens 2 and 4: 1/-f + 1/b = 1/f → b=-∞ so the light is parallel with x-axis after these lenses. For lens 1,3,5: 1/∞ + 1/b = 1/f → b=f so the projection is in the middle and for the last lens 25 away.

2)
I'm thinking the light is parallel to x-axis after the first lens because 1/f +1/b =1/f →
b=∞ and then for the second lens 1/∞ + 1/b = 1/f → image in f, so no magnification has occured.

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It's not certain both of my solutions are wrong, but probably both are :(.
If someone has a link to info about how to calculate lens after lens that would be great, I cant goggle it since I don't know what this sort of problem is called and my book is terrible.no help.

I am very happy for any help I can get, so thanks in advance.

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1) Seems okay. If you wanted to do this generally you could use ray matrices.

2) Yeah, if I read it right, I agree here too.

First; thank you for looking at my problems. But I did these 2 problems + 2 other and was told 3 out of 4 were wrong so both solutions can't be correct.

Well, I didn't fully understand your response to question 1, but the equivalent focal length is definitely 25, which is what you got.

I think you are right about Q2 too. A point source in the focal point of an ideal lens will give collimated light. So at this point you could put another lens at the end of a football field, and you'd get the same thing. The weird thing about this question is that it an image is captured at the focal point of the second lens. The other weird thing is that in technical terms a point source is a delta function, a point that is infinitely narrow, so it doesn't really even make sense to talk about it's magnification.

Maybe you can get some elaboration from your teacher on problem two, and I could help once I know what he/she wants.