Wave Physics - Optics - Effective Focal Length

[trocadero]

A lens system has seven lenses and each lens has the focal length 25mm. They are placed with a distance of 50mm between them. What is the effective focal length (EFL) of the system?

So we have the focal lengths:
f₁, f₂, ..., f₇ = 25mm
And the distance between the lenses:
d_1-2, d_2-3, ..., d_6-7 = 50mm

I have figured out that if the system would be afocal if it had an even number of these lenses. This is because the focal length of two adjacent lenses is the same as the distance between them. But since it's an uneven number it should have a focal length. I have drawn the light path of the system with only three of the lenses, but it is clear that the system repeats itself.
This image from wikipedia illustrates the light path between two of the lenses, except in my case f₁ = f₂ = 25mm and d = 50mm thus D₁ = D₂.

But I don't understand how to find the EFL. Using this formula for a three lens system to calculate it will of course result in division with zero.

Is there something else I can do with this information?

 

[drvrm]

But I don't understand how to find the EFL.

first you may try to analyse the ray diagram for two lenses given by you...it appears that a set of parallel rays is coming out as parallel from the 2nd lens...given the numbers try to figure out at what distance a set of parallel rays converge ...for all the seven lenses..then one can get the effective focal length.
your first lens is forming an image at 25mm...which works as an object for the 2nd lens...kept at focal length so each pair leads to a set of parallel rays only the last one converges at 25mm. try to work out the effective focal length.

 

[trocadero]

first you may try to analyse the ray diagram for two lenses given by you...it appears that a set of parallel rays is coming out as parallel from the 2nd lens...given the numbers try to figure out at what distance a set of parallel rays converge ...for all the seven lenses..then one can get the effective focal length.
your first lens is forming an image at 25mm...which works as an object for the 2nd lens...kept at focal length so each pair leads to a set of parallel rays only the last one converges at 25mm. try to work out the effective focal length.

Thank you for the reply. I'm thinking that since the rays converges at 25mm after the last lens it should mean that the effective focal length should be 25mm. The system is only repeating so the last lens should have the same effect on the rays as only a single 25mm lens. Or am I wrong?

 

[drvrm]

since the rays converges at 25mm after the last lens it should mean that the effective focal length should be 25mm.

please try the definition of 'focal length'...so it should be the distance from the 'lens system' to the focal point where the parallel rays converge...and it must be larger than 25 mm.
by the way did you get know why you were getting infinity when using some formulae quoted by you...its answer may be interesting...?

 

[trocadero]

please try the definition of 'focal length'...so it should be the distance from the 'lens system' to the focal point where the parallel rays converge...and it must be larger than 25 mm.
by the way did you get know why you were getting infinity when using some formulae quoted by you...its answer may be interesting...?

Thank you again!
So we have learned that if you extend the rays that have come through the last lens, they should cross where the rays originally came from at the position of the lens equivalent. And the distance from the lens equivalent to the focal point is the effective focal length. This picture illustrates that.

But the rays in my system that converges at 25mm after the last lens doesn't cross where they came from originally if I extend them. So does that mean that the focal length is infinity?

 

[drvrm]

But the rays in my system that converges at 25mm after the last lens doesn't cross where they came from originally if I extend them. So does that mean that the focal length is infinity?

by equivalent focal length of the system...one means that the parallel rays coming from left on the system produces an image of the object from which the rays are incident ...so you get an image at a finite distance ...so your focal length of the system is finite...the object is at infinity so that rays may be parallel...like pointing the system at Sun to catch its rays...or collimating rays from a source so that they are parallel or keeping the object at far off place so that its ;arge compared to the linear dimensions of system and distances from screen..

 

[trocadero]

by equivalent focal length of the system...one means that the parallel rays coming from left on the system produces an image of the object from which the rays are incident ...so you get an image at a finite distance ...so your focal length of the system is finite...the object is at infinity so that rays may be parallel...like pointing the system at Sun to catch its rays...or collimating rays from a source so that they are parallel or keeping the object at far off place so that its ;arge compared to the linear dimensions of system and distances from screen..

I'm sorry, but I still don't understand. So if the focal length is finite, it will be the distance from the lens equivalent to where the rays converge (25mm after the last lens). But where is the lens equivalent? At the position of the first lens? Then the focal length would be 50mm*6+25mm = 325mm. If it's not, how could I else calculate or draw where the lens equivalent should be?

 

[drvrm]

I'm sorry, but I still don't understand.

for understanding you must draw the ray diagram...imagine the lens system kept in a tube and get incident parallel rays from left in the tube then on the right hand from the edge you may get an image. so you can imagine a equivalent lens at the left edge and therefore the distance including the length of the tube... will give you focal length.
if you imagine the lens to be kept anywhere else then how you will have objects placed at different distances and can take images.
suppose you get incident parallel rays from the right end ...again one should get an image on the left distance 25mm from the left edge.

 

[trocadero]

so you can imagine a equivalent lens at the left edge and therefore the distance including the length of the tube... will give you focal length.

So if I understand you correctly, the first lens would be at the left edge of the tube. And the image will be 25mm to the right of the tube when rays are coming from the left. And since it's 50mm between each of the seven lenses the tube will be 300mm long. Then shouldn't the focal length be 325mm in total? I really don't get what I am missing here.

 

[drvrm]

Then shouldn't the focal length be 325mm in total? I really don't get what I am missing here.

by simple definition of focal length of a system of lenses it comes to same 325mm...however in your problem why one would put all those six lenses is not physically understandable to me ?

 

[trocadero]

by simple definition of focal length of a system of lenses it comes to same 325mm...however in your problem why one would put all those six lenses is not physically understandable to me ?

It's not a real world problem I think, the question is probably designed for us to research about focal length and understand afocal systems as well.
But you wrote six lenses, wouldn't 325mm be for seven lenses?

 

[drvrm]

But you wrote six lenses, wouldn't 325mm be for seven lenses?

yes the effective focal length of seven lenses will be 325 mm. i referred to those six which were so placed to render the rays parallel only.

 

[trocadero]

yes the effective focal length of seven lenses will be 325 mm. i referred to those six which were so placed to render the rays parallel only.

Ok, thank you so much for all of your help. I appreciate it! I've learned a whole lot in the process.