Question

A convex mirror used for rear-view on an automobile has a radius of curvature of $3.00\text{m}$. If a bus is located at $5.00\text{m}$ from this mirror, find the position $\&$ nature of the image.

• A. $v=1.15\text{m},$ virtual Image
• B. $v=1.5\text{m},$ virtual Image
• C. $v=0.86\text{m},$ virtual Image
• D. $v=0.86\text{m},$ real Image

Answer 1

The correct option is A $v=1.15\text{m},$ virtual Image

Radius of curvature $=3\text{m}$

We know that

Focal length $f=\frac{R}{2}=\frac{3}{2}=+1.5\text{m}$

[Since the focus of convex mirror is behind the mirror, the focal length will be positive].

Now,

Bus (object) is placed in front of the mirror.

$\therefore$ Object distance will be negative

Object distance $=u=-5\text{m}$

Let the image distance be ${}^{\prime }{v}^{\prime }.$

Then, $v=\frac{uf}{u-f}$
$\Rightarrow v=\frac{(-5)(+1.5)}{-5-1.5}\approx +1.15\text{m}$

In a convex mirror, virtual image is formed for a real object.
So, option (a) is correct.