What Is the Focal Length and Magnification in Multi-Lens Systems?

[sz0]

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.

------
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 can't 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.

 

[Mindscrape]

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.

 

[sz0]

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.

 

[Mindscrape]

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.

 

[asteriatic]

Hello,

I can provide you with some guidance on how to approach these problems and some resources that may be helpful.

First, for the first problem, you can use the thin lens equation: 1/f = 1/a + 1/b, where f is the focal length, a is the object distance, and b is the image distance. Since you have five lenses with the same focal length, you can use the equation to calculate the total focal length of the system. The object distance for each lens is 50, so you can plug in the values and solve for b. The final image distance will be the focal length of the system.

For the second problem, you can use the magnification equation: M = -b/a, where M is the magnification, b is the image distance, and a is the object distance. Since the light source is placed at the focal point of the first lens, the object distance will be 0. You can then use the image distance of the first lens as the object distance for the second lens and solve for the magnification. This will give you the final magnification of the system.

As for resources, there are many online tutorials and videos that can help you understand how to calculate lens after lens. Some helpful keywords to search for could be "thin lens equation", "magnification equation", and "multiple lens systems". Additionally, there are many textbooks and online resources that cover optics and lens calculations in detail, such as "Fundamentals of Optics" by Francis A. Jenkins and Harvey E. White.

I hope this helps! Let me know if you have any further questions or if you would like me to clarify anything. Good luck!