Mathematical Demonstration - Lenses in contact

[ToTalk]

Hi, I have been working on this for a little while and think I am approaching it incorrectly. If someone can help, I'd really appreciate it. This is for a basic introductory calculus based Physics class that I am in.

1. Mathematically demonstrate the following equation with no numerical examples



2. $$\frac{1}{f_{c}} = \frac{1}{f_{1}} + \frac{1}{f_{2}}$$ - This is the equation for the focal distance of two touching thin lenses.




3. I have tried using the lens equation for the first and second lens, and solving for a distance of zero between them, but i can't figure out how to solve for where the image from the first lens would be, and therefore how the second lens would act on it

Thanks Very Much.

 

[Kurdt]

Remove the slash before the 1 in the tex code. Try considering two lenses that are a distance d apart and having a look what happens. Wneh you have an equation for that see what happens when d tends to zero.

 

[ToTalk]

Hi Kurdt,

Thanks for the info.

Are you talking about this:

$$\frac{f_2 (d - f_1) } { d - (f_1 +f_2) }$$


If so, I had seen that, but I am unsure of how to get to that from the given equation.

Thanks

 

[Kurdt]

I am referring to that equation. Now as I say if you let d tend to zero you will obtain the equation you are after. I trust you know how to get to the equation with d.

 

[ToTalk]

Just got it. For some reason I distributed d to both terms in the numerator instead of $$f_{2}$$.

Thanks for your help.