A hair dresser stands with her nose $20 cm$ in front of a plane mirror for what distance must she focus her eyes in order to see her nose in the mirror?
A. $50cm$
B. $30cm$
C. $60cm$
D. $40cm$

Hint: A plane mirror forms images at the same distance behind it as the object is in front of it. So, the image will be formed at 20cm behind the mirror i.e. 40cm from the hairdresser.

Complete step by step answer:
We can make the following diagram according to the given situation.

Images formed by plane mirrors are virtual, upright, left-right reversed, the same distance from the mirror as the object's distance, and the same size as the object.
Plane mirrors are the sole variety of mirror that a true object always produces a picture that's virtual, erect and of the identical size because the object. Virtual objects produce real images. The focal distance of a plane mirror is infinity; its optical power is zero.
We know that a plane mirror forms an image at the same distance behind it as the object is in front of it. So, the image of the hair dresser’s nose will be formed at 20cm behind the mirror because her nose is at 20 cm in front of the mirror i.e. 20+20=40cm from the hair dresser’s eyes.

Hence,option D is the correct answer.

Note:Here, we can see that the hairdresser’s eyes and nose can be assumed to be at the same level i.e. 20 cm from the mirror. The point of nose and eye is just given so as to create a confusion in the solution, nothing else. The properties of a plane mirror that are to be kept in mind are given below.