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Suppose you wish to form an image of a 1cm wide object, 50cm away, on a sensor measuring 20mm. How can I calculate the magnification factor required and the focal length of the lens? I'm not sure how to begin.

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Please don't phrase your question as a command. What have you tried? You will get better assistance if you give everyone an idea of where you are stuck. – axblount Aug 29 '12 at 20:56
sorry man, its just that i have no idea of how to do this question – user1085773 Aug 29 '12 at 20:57
That's totally fine. You're probably best off just saying that flat out. Even a wild guess will usually give everyone an idea of where you're at. – axblount Aug 29 '12 at 21:05

Hint: If the object is 1 cm and the image is 20 mm, what is the magnification ratio? You should have a relation between object size, image size, object distance, and image distance-that will give you the image distance. Then you should have a relation between object distance, image distance and focal length. That will give you the focal length.

Added: The magnification factor is $m=\frac {20 \text{mm}}{1 \text{cm}}=2.$ Then let $d_o$ be the distance to the object, which is $50$ cm. Let $d_i$ be the distance to the image. $m=\frac {d_i}{d_o}=2$, so $d_i=100 cm$ $\frac 1f=\frac 1{d_o}+\frac 1{d_i}=\frac 1{50 \text{cm}}+\frac 1{100 \text {cm}}$. So $f = \frac {100}3 \text {cm}$

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