Question: I'd like to know how a basic lens combination can be formed into a simple refracting telescope, including how the calculations are made.
Answer: The simplest astronomical refractor will consist of two converging lenses and that is what we will look at here. The key step is to use the known focal lengths (we will use f1 = 10 cm and f2 = 20 cm) and then perform the necessary calculations. The trick is to find the image distance s1' for the first lens, then having done that find the object distance s2 of the second lens. One can also obtain the total magnification (lateral) using the magnification formula.
Before outlining the procedure we will use we need to set out the sign conventions to apply:
s is (+) if the object is in front of the lens
s is (-) if the object is in back of the lens
s' is (+) if the image is in back of the lens
s' is (-) if the image is in front of the lens.
Now the basic procedure in analyzing a thin lens combination is summarized here:
1) The image of the first lens (L1) is calculated as if the 2nd lens (L2) is not present.
2) The image of the first lens is treated as the object of the 2nd lens.
3) If the image of the first lens lies to the right of the 2nd lens, the image is treated as a virtual object for the 2nd lens (that is, s is negative).
4) The image of the 2nd lens is the final image of the system.
Now in pursuing the application we will use s1, s1' for lens L1 and s2, s2' for lens L2. We can refer to the diagram below:
Using the thin lens eqn. for lens L1:
1/s1 + 1/s1' = 1/15 + 1/s1' = 1/10 cm
therefore: s1' = 30 cm
e.g.: 1/ s1' = 1/15 - 1/10 = 5/150 or s1' = 150 cm/ 5
And for the 2nd lens:
1/s2 + 1/s2' = 1/f2
-> 1/ (-10 cm) + 1/s2' = 1/20 cm
or 1/s2' = 1/20 cm + 1/ 10 cm = 30 / 200 cm^-1 or s2' = 200/30 = (20/3) cm
Thus, the final image lies (20/3) cm to the right of the 2nd lens.
The lateral magnification for each lens is defined:
M1 = (-s1'/ s1) = - (30 cm/ 15 cm) = -2
M2 = (-s2'/s2) = -(20/3)cm/ -10 cm = 2/3
Then the total magnification of the lens system is:
M1 M2 = (-2)(2/3) = -4/3
So it is:
real, inverted and enlarged by 4/3 times over the object.
Again, the values used here are purely for instructional purposes, but there is no problem in generalizing the procedure for an actual, practical refracting telescope.