Question

a rear view mirror of an automobile has an focal length of 2 m if it locates a person standing at a distance 4m from it, find the nature and distance of the image.

Answer 1

Hope this will help lot the mirror is convex mirror

Answer 2

Answer:

The image distance is 1.33m, and is diminished, erect and virtual.

Explanation:

Given a convex mirror of focal length,  $f= 2 m$

         object distance,  $-u=4m$

According to sign convention, for convex mirror the object distance, as it is placed infront of the mirror.

Using mirror formula,

                    $\frac{1}{f} = \frac{1}{u} +\frac{1}{v} \implies\frac{1}{v} = \frac{1}{f} -\frac{1}{u}$

                                                 $= \frac{1}{2} -\frac{1}{-4}$

                                                 $= \frac{1}{2}+\frac{1}{4}$

                                                 $= \frac{2+1}{4}=\frac{3}{4}$

Therefore the image distance,

                     $v=\frac{4}{3}=1.33m$

The image distance is positive, hence the image is diminished, erect and virtual.