How does focal length affect magnification? My answer would be the longer the focal length, higher the magnification will be, resulting in a larger image. But in a ray diagram, how does it look? I am searching for a comparison of ray diagram between short focal length and long focal length but didn't manage to get anything. My high school textbook didn't explain much about focal length also. I wanted to know more about how does different focal length affect the image in a telescope as well. But Google shows only the simple ray diagrams. Thanks in advance.
 A: If you are using the lens as a magnifying glass the standard formula $\frac{1}{u}-\frac{1}{v}=\frac{1}{f}$, where $u$ and $v$ are the distances from the lens to the object and image respectively and $f$ is the focal length, together with the formula $m=\frac{v}{u}$, show that in theory you can get any desired magnification from any converging lens. In practice, to achieve a high magnification the object needs to be close to the focal point of the lens. This makes the image larger, but also further away. For high magnification with the image being fairly close you need a short focal length.
For a telescope the magnification is (objective focal length) / (eyepiece focal length). But for a good quality image neither can be too short. 
Standard ray tracing diagrams are a better approximation for longer focal lengths, because they assume a lens/mirror is flat, but still works like a curved mirror/lens.
A: NOTE: Lines are not straight and don't question the size of mirror and I have used concave mirror only.
In the image the position of the object is fixed (30cm) and two concave mirrors of focal length (20 and 10cm) are taken. 
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In the image it can be noticed that as focal length decreased the magnification also decreased . But it doesn't happen always.
Magnification is related to the focal length of the mirrors by using the formula
m=-(v/u) or it can be deduced to 
m= f/(f-u) {using sign convention}
For lenses it is
m=f/(f+u)
Thanks for asking.
