Question

An object is placed at a distance of $10cm$ from a convex mirror of focal length $15cm$. Find the position and nature of the image. 

Answer 1

Hint: First, use the equation that gives us the relation between the positions of the object, its image and focal length of the spherical mirror. Substitute the values according to the sign convection and calculate the position of the image. For the nature of the image check whether the value of v is positive or negative. 

Formula used:

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

$f$ is the focal length of the mirror.

$v$ and $u$ are the positions of the image and the object with respect to the pole of the mirror.

Complete step by step answer:

To find the position of the image we will use the equation that gives us the relation between the positions of the object, its image and focal length of the spherical mirror.

i.e. $\dfrac{1}{f}=\dfrac{1}{v}+\dfrac{1}{u}$   …. (i).

Here, f is the focal length of the mirror, v and u are the positions of the image and the object with respect to the pole of the mirror. These three values are according to the sign convection.

It is said that the object is placed in front of the mirror at a distance of 10cm. Therefore, $u=-10cm$.

The focal length of a convex mirror is always positive. Therefore, $f=15cm$.

Substitute the values of f and u in equation (i).

$\dfrac{1}{15}=\dfrac{1}{v}+\dfrac{1}{-10}$

$\dfrac{1}{v}=\dfrac{1}{15}+\dfrac{1}{10}$

$\Rightarrow\dfrac{1}{v} =\dfrac{25}{150}$

$\Rightarrow\dfrac{1}{v} =\dfrac{1}{6}$.

$\therefore v=6cm$.

When the $v$ is positive, the image is formed behind the mirror and when $v$ is negative, the image is formed in front of the mirror. This means that in this case the image is formed behind the mirror at a distance of 6cm from the pole of the mirror. When $v$ is positive, the image formed is virtual and when $v$ is negative, the image formed is real. In this case, since the value of $v$ is positive, a virtual image of the object is formed. Therefore Image formed will be virtual, erect and will form $6cm$ behind the mirror.

Note: We can also tell the nature of the image by the magnification of the image. If the magnification is positive, then the image formed is virtual. If the magnification is negative, then the image formed is real.