An object of height `1cm` is kept perpendicular to the principle axis of a convex mirror of radius of curvature `20cm`. IF the distance of the object form the mirror is `20 cm` then the distance (in `cm`) between heads of the image and the object will be:

Options

A. `sqrt((6404)/(9))`
B. `sqrt((6414)/(9))`
C. `(40)/(3)`
D. none of these

Answer

A

Explanation

`(1)/(v) = (1)/(f) - (1)/(u)`
`= (1)/(10) - (1)/((-20)) , v = + (20)/(3) cm`
`I = -(v)/(u) xx O = - ((20)/(3))/((-20)) xx 1 = (1)/(3)`
`:.` The distance between tip of the object and image is `= AC = sqrt((BC)^(2) + (AB)^(2))`
`S = sqrt((20 + (20)/(3))^(2) + (1 - (1)/(3))^(2)) = sqrt((6404)/(9)) cm`