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Obtain the relation between radius of cu...

Obtain the relation between radius of curvature and focal length of a concave mirror with necessary ray diagram.

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C-Centre of curvature
F-Principal Focus
R-Radius length of the mirror
`angleMCP=theta` and `angleMFP` =2`theta`
Now,tan `theta=(MD)/(CD)` and tan 2 `theta=(MD)/(FD)`
For small `theta,tantheta~~theta` and `tan2theta~~2theta`
Then ,`(MD)/(CD)=theta` and `(MD)/(FD)=2theta`
i.e., `(MD)/(FD)=2((MD)/(CD))impliesFD=(CD)/(2)`
For small `theta` ,the point D is very close to P.Applying sign conventions,FD =-f and CD=-R
Thus , `f=(R)/(2)`
Note :Full marks should be awarded for substituting .
FD=+f and CD=+R also
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