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

Given data: The focal length of the concave lens f = 20 cm, Magnification m = 3
First case : When the image is virtual, m = 3
Magnification m = ` (-v)/(u) = 3`
`i.e (-v)/(u) = 3`
` v= -3u`
According to mirror formula :
` 1/f = 1/u + 1/v`
` (1)/(-20) = 1/u - (1)/(3u)`
`(1)/(-20) = (3-1)/(3u)`
` (3u)/(2) = -20 " " therefore u = (-40)/(3)`
` u = (-40)/(3) cm `
` therefore v = - 3 xx (40/3)`
` = - 40 cm`
The distance of image from the mirror when the image is virtual is 39.9 cm.
Second case : When the image is real, m = -3
Magnification, m ` = (-v)/(u)`
` (-v)/(u) = -3`
` v = 3 u`
According to mirror formula
` 1/f = 1/u + 1/v`
` (1)/(-20) = 1/u + (1)/(3u)`
` (1)/(-20) = (3 + 1)/(3u)`
` (3u)/(4) = -20`
`3u = -80`
Two possible distance of the object from the mirror are `(-40)/(3) ` and ` (-80)/(3) cm` .