An object 5cm is placed at a distance of 20 cm in front of a convex mirror of radius of curvature 30 cm. Find the position, nature and size of the image.

Explanation

Object distance, `u=-20 cm`
Object height h = 5 cm
Radius of curvature, R = 30 cm
Radius of curvature = 2 * Focal length
R = 2 f, f = 15 cm
According to the mirror formula.
`(1)/(v)-(1)/(u)=(1)/(f)`
`(1)/(v)=(1)/(f)+(1)/(u)=(1)/(15)+(1)/(20)=(4+3)/(60)=(7)/(60)`
V = 8.57 cm.
The positive value of indicates that the image is formed behind the mirror.
Magnification :
`m=("Image Distance")/("Object Distance")=(-8.57)/(-20)=0.428`
The positive magnification indicates that the image formed is virtual.
Magnification, `m=("Height of the Image")/("Height of the Object")=(h^(1))/(h)`
`h^(1)=m xx h = 0.428xx5=2.14 cm`.