A shop security mirror 5.0 m from certain items displayed in the shop produces on-tenth magnification.
What is the radius of curvature of the mirror?
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Solution
Given,
Distance of the object (u) = -5 m
Distance of the object (u) = -5 m
Magnification (m) = `1/10`
We have to find the position of the image (v), radius of curvature (R) and the focal length of the mirror (f).
Using the magnification formula, we get
`m=(-v)/u`
Using the magnification formula, we get
`m=(-v)/u`
`m=(-v)/-5`
`1/10=(-v)/-5`
`1/10=v/5`
`v=0.5 m`
Now, using the mirrorformula, we get
`1/f=1/u+1/v`
`1/f=1/-5+1/0.5`
`1/f=1/-5+10/5`
`1/f=-1/5+10/5`
`1/f=9/5`
`f=5/9`
`R=2f`
`R=10/9`
or, R = 1.1
Therefore, the radius of curvature of the mirror (R) is 1.1 m.
Concept: Convex Mirror
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