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

u = - 12 cm , f = 15 cm , `h_(0) = 4.5` cm
` (1)/(v) + (1)/(u) = (1)/(f) , (1)/(v) + (1)/((-12)) = (1)/(15) " " v = (15 xx 12)/(15 + 12) = (15 xx 12)/(27) = (20)/(3) = 6.67` cm
Image is 6.67 cm behind the mirror . M = `(h_(i))/(h_(0)) = (-v)/(u) , (h_(i))/(4.5) = ( - ((20)/(3)) )/(12) = (20)/(3 xx 12) = (5)/(9)`
`h_(i) = (5 xx 4.9)/(9) = 2.5 ` cm
image is virtual , erect and diminished