An object is placed in front of a concave mirror of focal length 20 cm. The image formed is three times the size of the object. Calculate two possible distances of the object from the mirror.

Explanation

m = + 3 and m = - 3, f = - 20cm
When, m = 3
`m = - (v)/(u) = 3`
v = - 3 u
From mirror equation,
`(1)/(f) = (1)/(v) + (1)/(u)`
`(1)/(-20) = (1)/(-3u) + (1)/(u)`
`=(1)/(u)[-(1)/(3)+1]`
`(1)/(-20) = (2)/(3u)`
`u = - (40)/(3) cm`
When, `m =- 3 rArr v = 3u`
`(1)/(f) = (1)/(v) + (1)/(u)`
`(1)/(-20) = (1)/(3u) + (1)/(u)`
`(1)/(-20) = (4)/(3u)`
`u = - (4 xx 20)/(3)`
` u = - (80)/(3) cm`