A 4.5 cm needle is placed 12 cm away from a convex mirror of focal length 15 cm. Give the location of the image and the magnification. Describe what happens as the needle is moved farther from the mirror.

Explanation

`rArr` Here, height of pin `h_1 = 4.5 cm`
Object distance u = -12 cm
Focal lenght of convex mirro f = + 15 cm
`rArr` Mirror equation,
`1/f = 1/u + 1/v`
`therefore 1/v = 1/f - 1/u = 1/ (+15) - 1/(-12)`
`therefore v = 60 / 9 cm = 20/3 cm `
`therefore v = + 6.67 cm`
`rArr` Image distance is positive. Hence, image is virtual and erect and behind mirror at 6.67 cm
Magnification `m = - v/u = - (20)/(-3 xx 12) = +0.56`
`(h_2)/(h_1) = - (20)/(3 xx (-12)) = 5/9`
`therefore h_2 = 5/9 xx h_1 = 5/9 xx 4.5 = 2.5 cm `
`rArr` When pin is taken away from mirror F, then image will become smaller.