Question

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? 

Answer 1

 Given,
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` 

`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.