A convex mirror of focal length f produced an image `(1//n)^(th)` of the size of the object. The distance of the object from the mirror is

Options

A. (n-1) f
B. `((n-1)/(n))` f
C. `((n+1)/(n))` f
D. (n+1) f

Answer

A

Explanation

Magnification(m) =`(1)/(n)`
`rArr " " (-v)/(u) = (1)/(n) rArr v = (-u)/(n)`
Mirror formula,
`(1)/(v) + (1)/(u) = (1)/(f) rArr (1)/(u) = (1)/(f) - (1)/(v) = (1)/(f) + (n)/(u)`
`rArr (1)/(u) - (n)/(u) = (1)/(f) rArr (1)/(u) (1- n) = (1)/(f) rArr (u)/(1- n) = f `
`rArr u = f(1 -n)`
`rArr u = - f(n -1) ` and distance is | -f(n-1) | = f(n- 1).