Question

An object of 4 cm length is placed at a distance of 18 cm in front of a convex mirror of radius of curvature 30 cm. Find the position of the image ,its nature and size?​

Answer 1

The position is 8.18cm from the mirror.

Nature is b=virtual

Size is 1.82cm

Step-by-step explanation:

Note that for a convex mirror, the image distance and the focal length are negative;

Given

Object height H0 = 4cm

object distance u = 18cm

Radius of curvature R = 30cm

Since f = R/2

f = 30/2

f = -15cm

Recall that:

`(1)/(f) =(1)/(u)+ (1)/(v)\\(1)/(-15)=(1)/(18)+(1)/(v) \\(1)/(v) =(1)/(-15) -(1)/(18)\\ (1)/(v) = (-18-15)/(270)\\(1)/(v) = (-33)/(270)\\v=(-270)/(33)\\v=-8.18cm`

Since the image distance is negative, this shows that the image is a virtual image.

To get the size:

`(H_1)/(H_0)=(v)/(u)\\(H_1)/(4)=(8.18)/(18)\\18H_i=32.72\\H_i=(32.72)/(18)\\H_i= 1.82cm`