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.

Options

A. 12 cm
B. 24 cm
C. 36 cm
D. 48 cm

Answer

C

Explanation

On screen real image is obtained
`m=-3,u=-x,m=-(v)/(u)`
`-3=-(v)/(-x)impliesv=-3x`
`(1)/(f)=(1)/(v)+(1)/(u)=(1)/(-3x)+(1)/(-x)=-(4)/(3x)` …..(i)
As size of image is decreased i.e., object is moved away.
`m=-2,u=-(x+6),v=-2(x+6)`
`(1)/(f)=(1)/(v)+(1)/(u)=(1)/(-2(x+6))+(1)/(-(x+6))=(-3)/(2(x+6))` ..(ii)
`-(4)/(3x)=-(3)/(2(x+6))implies8(x+6)=9x`
`x=48cm`
`(1)/(f)=-(4)/(3x)=-(4)/(3xx48)impliesf=-36cm`