The image of the flame of a candle due to a mirror is formed on a screen at a distance of 9cm from the candle. The image is magnified 4 times. Determine the nature, position and focal length of the mirror.

Explanation

As a magnified image is formed on a screen, the image is real.

Let u=-xcm and hence `v=-(x+9)cm`
`"Here", " " m=4 or, (v)/(u)=4` [taking only the mod value of m]
`or, " " (x+9)/(x)=4 or, 4x=x+9 or, x=3`
`therefore " " u=-3cm`
So, the mirror is situated at a distance of 3 cm from that flame.
`"Now" " " ,v=-(3+9)=-12cm`
`"We know" " " (1)/(v)+(1)/(u)=(1)/(f) or, (1)/(-12)+(1)/(3)=(1)/(f)`
`or, " " -((1+4)/(12))=(1)/(f) or, f=-(12)/(5)=-2.4cm`
So, the focal lenght of the mirror is 2.4 cm. its negative sign indicates the nature of the mirror as a concave one [Fig.1.40].