Question

When an object is placed at a distance of 50 cm from a concave spherical mirror, the magnification produced is, `-1/2`. Where should the object be placed to get a magnification of, `-1/5`? 

Answer 1

Given,
Magnification `(m)=-1/2`

Distance of the object (u) = −50 cm

We have to find the distance of the object when the magnification is `=-1/5`
Therefore, using the magnification formula, we get  

`m=-v/u` 

v=-mu 

`v=-(-1/2xx-50) ` 

`v=-25` cm 

Now, using the mirror formula, we get 

`1/f=1/u+1/v` 

`1/f=1/-"mu"+1/u` 

`1/f=1/-25+1/-50` 

or` 1/f=-2/50-1/50=3/-50` 

or `f=-50/3` cm 

Now,
Magnification = `m=-1/5`

Therefore, using the mirror formula, we get 

`1/f=1/-"mu"+1/u` 

`or -3/50=(-5)/-5+1/u` 

`or (-3)/50=5/u+1/u` 

`or (-3)/50 =6/4` 

`u=-50xx6/3=-100` cm  

The object should be placed in front of the mirror at a distance of 100 cm to get the magnefiction of `-1/5`