Answer:
The distance between the object and the mirror is X/2
Explanation:
If we look into a plane mirror, we see the image of our face situated behind the mirror. Now, if we move backwards, the image also moves backwards in the mirror so that it is always at the same distance behind the mirror as our face is in front of the mirror. Thus, the image I in a plane mirror is as far behind the mirror as the object O is in front of it. In other words, the distance of the image from the plane mirror is equal to the distance of the object from the plane mirror. We will prove this fact by using the laws of reflection and simple geometry.
From the second law of reflection, we have:Angle of incidence = Angle of reflection
So, NAO = NAX (angle i = angle r)
It is clear that the triangles MIA and MOA are congruent triangles and, therefore, their corresponding sides should be equal. Thus :
IM = OM
MA is a common side to both triangles
Now, OM represents the distance of object from the mirror, and IM represents the distance of image from the mirror .
So, we can now say that:
Distance of image from mirror = Distance of object from mirror
