A concave mirror has a focal length of 20 cm. Find the position or positions of an object for which the image-size is double of the object-size.

Explanation

Let distance of object from mirror is `x`
`f=-20cm`
Image height is double of object height. The image may be If image is real
`m=-2`
`m=-(v)/(u)implies-2=-(v)/(-x)impliesv=-2x`
`(1)/(v)+(1)/(u)=(1)/(f)implies(1)/(-2x)+(1)/(-x)=(1)/(-20)implies(1+2)/(2x)=(1)/(20)`
`x=30cm`
If image is virtual
`m=+2`
`m=-(v)/(u)implies2=-(v)/(-x)impliesv=2x`
`(1)/(v)+(1)/(u)=(1)/(f)implies(1)/(2x)+(1)/(-x)=(1)/(-20)implies(1-2)/(2x)=(1)/(-20)`