Question

An object is placed at a distance of 20 cm from a concave mirror of radius of curvature 0.6 m. Which of the following statement is incorrect?

• A. The image is formed at a distance of 60 cm from the mirror.
• B. The image formed is real.
• C. Magnitude of image distance = 3times of magnitude of object distance.
• D. The image formed is upside down.

Answer 1

The correct option is B The image formed is real.

Given :
Radius of curvature $R$ = 0.6 m = 60 cm
Let $f$ be the focal length
We know that
$f=\frac{R}{2}$
$f=30cm$
For a concave mirror, focal length is taken as negative
i.e $f=-30cm$

So, formed image is virtual.
As

Object distance $u=-20cm$
Let $v$ be the image distance
Using mirror formula,
$\frac{1}{\text{f}}$ = $\frac{1}{\text{v}}$ + $\frac{1}{\text{u}}$
$\frac{1}{\text{-30}}$ = $\frac{1}{\text{v}}$ + $\frac{1}{\text{-20}}$
$\Rightarrow \frac{1}{\text{v}}=\frac{1}{\text{-30}}$ + $\frac{1}{\text{20}}$
$\Rightarrow v=60cm$

Positive sign of v indicates that image is virtual and as both u and v are with same sign, so, the image will be erect.