Three convex lens problem

[Geocentric]

# Three convex lens of focal length 10 cm each are mounted coaxially as shown in figure. An object O is placed at a distance of 20 cm from L1 and the final image formed is at a distance of 20 cm from L3. What is the distance L1L2?

Please help me with this problem. If the distance L2L3 was given this problem could be easily solved. But without that value, how to solve this problem?

[sebbysteiny]

If the distance L2L3 was given this problem could be easily solved. But without that value, how to solve this problem?

 

Looking at the problem, there is only one position L2 can be: Exactly half way between L1 and L3 by symetry. Thus, L1L2 = L2L3.

 

If you need any more help, let me know.

[Tim_Lou]

"as shown in the figure"...

 

perhaps you can post a figure here?

[Geocentric]

"as shown in the figure"...

 

perhaps you can post a figure here?

i am sorry, i typed it by mistake.

[Geocentric]

Looking at the problem, there is only one position L2 can be: Exactly half way between L1 and L3 by symetry. Thus, L1L2 = L2L3.

 

If you need any more help, let me know.

Is there an expression to find the equivalent focal length of 3 lenses placed coaxially?

[Tim_Lou]

if im not mistaken, you can probably calculate the focal length of the first 2 lens, then treat it as one lens, and calculate the focal length combining with the third one.

 

this is probably the equation you'll need:

http://scienceworld.wolfram.com/physics/ThinLensDoublet.html

 

as optics is not my area of physics....

well, probably you'll need some algebraic manipulations of this equation.