Murugan trims his beard while looking into a concave mirror whose focal length is $18cm$. He looks into it from a distance of $12cm$
i.How far is Murugan's image from the u?
ii.Does it matter whether or not Murugans face is closer or farther than the focal length? Explain.

Hint: To solve this problem we should learn about the Concave mirror, Mirror formula and the concept behind them. Then we can use this information for easily approaching our answer.

Complete answer:
Concave mirror: A concave mirror which is also called converging mirror, having a reflected surface bulging inward. They are used to focus light.
Concave mirrors are used for producing both real and virtual images. They can be upright or inverted.
Mirror formula: Mirror formula is defined as the equation related object distance and image distance with focal length is known as a mirror equation .It is also known as mirror formula.
Focal length: The focal length of an optical system is an estimate how strongly it converges or diverges light. A $ + $ focal length indicates that a system converges light, while a $ - $ focal length indicates that the system diverges light.

Given,
Focal length is $18cm$ .
Distance =$12cm$ .
To find the distance of Murugan’s image from the mirror and to find whether it matters if Murugans face is closer or farther than the focal length.
According to the given criteria,
Focal length of concave mirror, $f = - 18cm$
Object distance, $u = - 12cm$
Applying lens formula,
$\dfrac{1}{f} = \dfrac{1}{v} + \dfrac{1}{u}$
$ \Rightarrow \dfrac{1}{v} = \dfrac{1}{u} - \dfrac{1}{f}$
$ \Rightarrow \dfrac{1}{v} = \dfrac{1}{{ - 12}} - \dfrac{1}{{ - 18}}$
$ \Rightarrow \dfrac{1}{v} = \dfrac{{ - 3 + 2}}{{36}}$
$ \Rightarrow v = - 36cm$

i.Hence Murugan’s image is formed $36cm$ behind the concave mirror.
ii.Yes it matters whether his face is closer or farther than the focal length as when his face is closer to focal length of a concave mirror, then an enlarged image of the face is seen in the concave mirror that helps him in making a smooth shave. On the other hand, If his face is farther than the focal length an inverted, real image will be formed. So, his face will not be visible in the mirror.

Note: Concave mirrors reflect light inward to the one focal light. They are mostly used to focus light. A concave mirror shows different images types depending on the distance between the mirror and the object. Concave mirror is used in a shaving mirror, used in ophthalmoscope, used in astronomical telescopes, used in headlight.