A concave mirror forms a real image three times larger than the object on a screen. The object and screen are moved until the image becomes twice the size of the object. If the shift of the object is 6cm, find the shift of screen.

Explanation

Let distance of object from mirror is `x`
`m=-3,u=-x`
`m=-(v)/(u)`
`-3=(-v)/(-x)`
`v=-3x`
`(1)/(f)=(1)/(v)+(1)/(u)=(1)/(-3x)+(1)/(-x)=-(4)/(3x)`
`f=-(3x)/(4)`
When real object is moved towards the mirror, real image moves away from mirror and becomes arger. Here image height becomes double from triple i.e., object is moved away from mirror.
`u=-(x+6),m=-2,v=-2(x+6)`
`(1)/(f)=(1)/(v)+(1)/(u)=(1)/(-2(x+6))+(1)/(-(x+6))=-(3)/(2(x+6))`
`(1)/((-3x)/(4))=-(3)/(-2(x+6))implies(4)/(3x)=(3)/(2(x+6))`
`8x+48=9x rArr x=48cm`
`f=-(3x)/(4)=-(3)/(4)xx48=-36cm`
Distance by which screen is shifted
`=3x-2(x+6)=x-12=48-12=36cm`