Question

An object $1cm$ high produces a real image $1.5cm$ high when placed at a distance of $15cm$ from a concave mirror. The position of the image is:
A) 22.5cm in front of the mirror
B) 22.5cm behind the mirror
C) 45cm in front of the mirror
D) None of the above

Answer 1

Hint: Concave mirror has a surface that is curved inwards, concave mirror have the formula to calculate the focal length of the mirror as:
$\dfrac{1}{f} = \dfrac{1}{u} + \dfrac{1}{v}$ (Position of object from the mirror is given by u, position of image is given by v, f represents the focal length)
Relation between the size of image and object and distance of image and object is given as:
$ - \dfrac{v}{u} = - \dfrac{{{h_i}}}{{{h_o}}}$ ( hi and ho are height of the image and object)
Using the above relations we will bring out the position of image formation.

Complete step by step solution:
Let's discuss the properties of concave mirrors first and then we will calculate the position of the image.
Concave mirror is also known as a converging mirror because it tends to focus light which falls on it. Image formed by a concave mirror is virtual as well as real. Concave mirror shows different image sizes depending upon the position of the object.
Now let's calculate the position of the image formed by the concave mirror.
All the distances are measured in the direction of incident light and are taken as positive distances measured opposite to the direction of incident light are taken as negative.
Relation of size of the image, object and position of the image, object is given as;
$ \Rightarrow - \dfrac{v}{u} = - \dfrac{{{h_i}}}{{{h_o}}}$
We will substitute the values all the parameters given to us
$ \Rightarrow \dfrac{{ - v}}{{ - 15}} = - \dfrac{{1.5}}{1}$(We will take the distance of object as negative)
$ \Rightarrow v = - (15 \times \dfrac{{1.5}}{1})$
$ \Rightarrow v = - 22.5cm$
We obtained the distance of the image position as negative this means that the image formed in front of the mirror.

Thus, option (A) is correct.

Note: Concave mirror have many applications in various fields such as used as dental mirror to get magnified image of the teeth for better vision, used in headlamps, torches, spot lights, concave mirrors concentrate solar power so used in various solar power equipments to converge the light falling on it.