A virtual image of magnification +5.0 is produced when an object is placed 5.0cm in front of a concave mirror. Find the radius of curvature of the mirror. Draw a ray diagram to verify your numbers.
given , magnification = 5
we have equation for magnification m = - di/do
where di is the distance of image
do is the distance of object
also given, do = -5 cm ( for a concave mirror , distance of object is taken negative)
substituting in m we get, 5= - di/ -5
5× -5 = -di
di = 25 cm
Now we have lens formula 1/f = 1/ do+ 1/ di
where f = focal length
substituting for do and di we get,
1/f = 1/-5 + 1/25
1/f = 1/25 -1/5
=( 5-25)/25 = -4/25
or f = -25/4 = -6.25 m
Our objective is to find radius of curvature.
we have , focal length , f = R /2
so R = 2f = -2×6.25 =- 12.5 m.
so radius of curvature is 12.5 m.
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