At what distance from a convex mirror of focal length 30 cm should an object be placed so that its image is formed 20 cm from the mirror on the other side?

Text Solution

Solution : In the given problem <br> Object distance, u = - 30 cm (from sign convention) <br> Image distance, v = ? <br> Focal length of the lens f = 20 cm <br> From lens formula <br> ` 1/f=1/v-1/u` <br> ` 1/20 = 1/v - 1/(-30)` <br> `1/20 = 1/v + 1/30` <br> ` 1/v = 1/20 - 1/30` <br> ` 1/v = (30-20)/(30 xx 20) = (10)/(600) ` <br> ` v = (600)/10 = 60 ` cm . <br> Magnification, m = `("height of the image")/("height of the object ") = v/u` <br> ` M = (60)/(-30)= - 2`. <br> Negative sign indicates that the image is inverted . Since, m is greater than one, the image is magnified. <br> Since v is positive, the image is real. <br> The image is formed 60 cm on the other side of the lens and it is real, inverted and magnified.