Question

A convex mirror used as rear view mirror on an automobile has a radius of curvature of 3.00 m. If a bus is located at 5.00 m from this mirror, find the position, nature and size of the image.

Answer 1

Given,

Object distance (u)= -5 m (always negative)
Radius of curvature C = 3 m
Focal length = 3/2 = 1.5 m.
From the mirror formula,

We know,

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

Putting all the values

$\frac{1}{v}-\frac{1}{5}=\frac{1}{1.5}$

$\frac{1}{v}=\frac{10}{15}+\frac{1}{5}=\frac{13}{15}$

After solving

$v=1.15m$

Now we have to find the magnification

We know,

$m=\frac{-v}{u}$

Putting all the values

$m=\frac{-1.15}{-5}$

After solving

m = 0.23
The image distance is positive this means it is formed on right side of the pole i.e. on the opposite side of the object. Here magnification is positive and less than 1 so it will be virtual, erect and smaller than size of object.
So the image is formed at 1.15m from mirror on right side and it is virtual, diminished, and erect.