Final answer:
To prove that the distance of the image is equal to the distance of the object from the mirror,c. the mirror formula is applied to a flat mirror
Step-by-step explanation:
To prove that the distance of the image is equal to the distance of the object from the mirror using the mirror formula, we can apply it to a flat mirror scenario. The mirror equation relates object distance (do), image distance (di), and focal length (f). For a flat mirror, the focal length is at infinity because the radius of curvature is infinite. This simplifies the mirror equation, leading us to conclude that the object and image are equidistant from the mirror, and because a flat mirror does not curve, it does not alter the paths of the reflected rays in a way to change the distances.
Ray tracing for a flat mirror shows that the angles of incidence and reflection are equal, making the path lengths the same, which corresponds to the concept that di = -do. This negative sign indicates that the image formed is a virtual image that appears to be behind the mirror.
A practical example confirming this phenomenon is when we use a flat mirror, our image appears to be the same distance behind the mirror as we stand in front of it, and this is a fundamental principle used in everyday situations like checking our reflection. We do not need to use other formulas or laws such as Snell's law here, as it pertains to refraction, not reflection.