A 5 cm tall object is placed at a distance of 30 cm from a convex mirror of focal length 15 cm. Find the position, size and nature of the image formed.

Explanation

In the given convex mirror-
Object height ,` h_(1) = + 5 "cm" ` Object distance, u = - 30 cm,
Foral length, f= + 15 cm , Image distance , v= ?
Image height ` , h_(2)` = ?
Nature = ?
According to mirror formula ,
` 1/v + 1/u = 1/f Rightarrow 1/v + 1/(-30) = 1/(+15)`
` 1/v= 1/15 + 1/30 = ( 2+ 1)/30 = 3/30 =1/10 therefore ` v = + 10 cm
The image is formed (10 cm) behind the convex mirror. Since the image is formed behind the convex mirror, its nature will be virtual (as v is +ve).
` h_(2)/h_(1) = (-v)/u Rightarrow h_(2)/5 = (-(1+10))/(-30)`
` h_(2) = 10/30 xx 5 therefore h_(2) 5/3 = + 1.66 cm`
Thus size of the image is 1.66 cm and it is erect (as ` h_(2)` is + ve)
Nature of image = Virtual and erect