In order to get some ideas as to what type of numbers to choose, I used an example in my Optics textbook and extimated some values for focal length. Also, I noticed a term in the bottom left entry that would make x independent from y.
First of all, the textbook suggested values of 35cm and 10mm for the focal lengths of the first and second lenses, respectively. Next, looking at the bottom left entry, I recognized that, by letting the focal length of the third lens equal the distance from the third lens to the image, I could eliminate the y 's from the equation. (*Go to the previous section to check if you can see why this works.) I let both of these distances equal 25mm. Finally, I chose some arbitrary distance to the object: 100m.
Now that we've chosen these values, we are ready to check to see how our zoom lens works!
X vs. Y
The graph verifies the fact the x is independent from y. That is to say, no matter what value of y, x is the same.
Power vs. Y
This graph illustrates the linear relationship between Power and y. Though it is very difficult to see on the graph, we have Power = 1 when y = 19cm. Making 19cm be the smallest we allow y to get, we have Power ranging from 1 to 80.
If you have comments or suggestions, email me at firstname.lastname@example.org
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