Question

In a car a rear view mirror having a radius of curvature 1.50 m forms a virtual image of a bus located 10.0 m from the mirror. The factor by which the mirror magnifies the size of the bus is close to

• A. 0.06
• B. 0.07
• C. 0.08
• D. 0.09

Answer 1

The correct option is B 0.07

The rear view mirror is a convex mirror.

Given:

Radius of curvature $R=+1.50m$

Focal length $f=\frac{R}{2}=\frac{+1.50}{2}=+0.75m$

Object distance $u=-10m$

By mirror formula,

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

$\Rightarrow \frac{1}{0.75}=\frac{1}{v}+\frac{1}{-10}$

$\Rightarrow \frac{1}{v}=\frac{10+0.75}{7.5}=\frac{10.75}{7.5}$

$\Rightarrow v=\frac{750}{1075}=\frac{30}{43}m$

Magnification $m=-\frac{v}{u}=-\frac{30}{43}\times \frac{1}{(-10)}$

$\therefore m=+0.069\approx +0.07$

Option B is correct.