Question

A moth at about eye level is $10\,cm$ in front of a plane mirror; you are behind the moth, $30\,cm$ from the mirror. What is the distance between your eyes and the apparent position of the moth's image in the mirror ?

Answer 1

Hint: In order to this question, to find the distance between your eyes and the apparent position of the moths image in the mirror, first we will rewrite the image distance and the object distance, and then we will find the distance between the object and the position where image formed.

Complete step by step answer:
As per the question, the image of the moth is $10\,cm$ behind the mirror and we are $30\,cm$ in front of the mirror.
So, the image distance is, $v = 10\,cm$
and, the object distance is, $O = 30\,cm$
Therefore, we must focus our eyes for a distance of $|v| + |O|$ ;
i.e.. $10\,cm + 30\,cm = 40\,cm$

Hence, the distance between your eyes and the apparent position of the moth's image in the mirror is $40\,cm$.

Additional-Information: The object distance is defined as the distance between the object and the point of incidence on the mirror. Image distance is the distance between the point of incidence of the mirror and where the image is produced. Furthermore, for plane mirrors, this image behind the mirror is usually created at a distance equal to the distance the object is put in front of the mirror. As a result, the image distance equals the object distance. However, this isn't true for all sorts of mirrors.

Note: The picture distance in the eye does not vary when the distance between an item and the eye increases. The focal length of the eye lens is adjusted as a result of the eye's accommodation power, which compensates for the increase in object distance. The image distance remains constant, and the image is produced on the eye's retina.