Question

A candle is placed inside the focal point of a concave mirror. Which of the following options describes the characteristics of the image.
A) Virtual, erect and reduced
B) Virtual, erect and magnified
C) Virtual, inverted and reduced
D) Real, erect and reduced
E) Real, inverted and magnified

Answer 1

Here the object lies within the focal point of the mirror and so the distance of the object from the concave mirror will be less than the focal length of the mirror. Using the mirror equation we can determine whether the image is real or virtual. Also if the magnification is positive and greater than one the image formed will be erect and magnified.

Formula Used:
1)The mirror equation is given by, $\dfrac{1}{v} - \dfrac{1}{u} = \dfrac{1}{f}$ where $v$ is the image distance, $u$ is the object distance and $f$ is the focal length of the mirror.
2)The magnification of a mirror is given by, $m = \dfrac{{ - v}}{u}$ where $v$ is the image distance and $u$ is the object distance.

Complete step by step answer:
Step 1: Using the mirror equation determine the image distance.
It is given that the object lies within the focal point of the concave mirror.
$\Rightarrow \left| f \right| > \left| u \right|$
The mirror equation is given by, $\dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f}$ where $v$ is the image distance, $u$ is the object distance and $f$ is the focal length of the mirror.
Now by sign convention, the mirror equation of the concave mirror will be $\dfrac{1}{v} - \dfrac{1}{u} = - \dfrac{1}{f}$
$\Rightarrow \dfrac{1}{v} = \dfrac{1}{u} - \dfrac{1}{f}$ or we have $v = \dfrac{{f - u}}{{uf}}$
Since it is mentioned that $\left| f \right| > \left| u \right|$, $f - u = + {\text{ve}}$ and so the image distance $v$ is positive and $v > \left| u \right|$ .
Thus the image formed is virtual.
Step 2: Using the relation for the magnification of the concave mirror determines the nature of the mirror.
The magnification of a mirror is given by, $m = \dfrac{{ - v}}{u}$ where $v$ is the image distance and $u$ is the object distance.
Then by sign convention, we have the magnification $m = \dfrac{{ - v}}{{ - u}} > + 1$ as $v > \left| u \right|$ .
This suggests that the image formed is erect and magnified.
So the image formed is virtual, erect and magnified.
Thus the correct option is B.

Note: For a concave mirror, the object distance $u$ and focal length of the mirror $f$ lie to the left of the concave mirror i.e., on the negative X-axis and so are negative. To the right (or behind) of the concave mirror, distances are taken to be positive. An image formed is said to be virtual if it is formed behind the mirror and it is said to be real if it is formed in front of the mirror. Here the image distance is positive and so lies behind the mirror.