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Toby_phys
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Homework Statement
Homework Equations
We will call ##s## the distance of the object from the first lens, ##s'## the distance of the image from the first lens and ##s''## the distance of the image from the second lens.
The Gauss's lens equation:
$$\frac{1}{s} +\frac{1}{s'}=\frac{1}{f_1}$$
The Attempt at a Solution
Using Gauss's lens equation we get:
$$s'=\frac{sf_1}{s-f_1} $$we can use the image from the first lens as the object for the second lens.
$$\frac{-1}{s'-d}+\frac{1}{s''}=\frac{1}{f_2} $$
Note - I feel my mistake is here, I think my algebra is correct after this.
This gets us:
$$ \frac{1}{s''}=\frac{1}{f_2}+\frac{1}{s'-d}=\frac{s-f_1}{sf_1-sd+f_1d}+\frac{1}{f_2}$$
The total focal length is given by:
$$\frac{1}{f}=\frac{1}{s}+\frac{1}{s''}=\frac{1}{s}+\frac{1}{f_2}+\frac{s-f_1}{sf_1-sd+f_1d}$$
Which doesn't get the desired result. Thank you in advance