Question

A convex mirror used for rear-view on an automobile has a radius of curvature of 3:00 m. if bus is located at 5:00 m form this mirror, find the position, nature and side of the image.

Answer 1

$\huge\mathfrak{solution}$

Here,

radius of curvature of the convex mirror, R = +3.00m and distance of the object (bus) from the mirror, u = -5.00 m

focal length of the mirror,

$f = \frac{r}{2} = + \frac{3.00}{2} = + 1.50 \: m$

since,

$\frac{1}{v } + \frac{1}{u} = \frac{1}{f} \: \: hence,$

$\frac{1}{v} = \frac{1}{f} - \frac{1}{u} = \frac{1}{( + 1.50)} - \frac{1}{( - 5.00)}$

$= \frac{5.0 + 1.5}{1.5 \times 5.0}$

$v \: = \frac{1.5 \times 5.0}{(5.0 + 1.5)} = \frac{7.5}{6.5}$

$\bold{= 1.15m}$

Plus (+) sign of v signifies that the image is formed behind the mirror and is a virtual erect image.

Moreover,

magnification, m = h'/h = -v/u = -(+1.15)/(-5.0)

= +0.23

h' = +0.23h

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