Physics · Ch 6 — Optics
Characteristics of the Image Formed by Plane Mirror
Characteristics of the Image Formed by Plane Mirror
A plane mirror's image has four defining characteristics: it is virtual (cannot be projected onto a screen), erect (right-way up), laterally inverted (left and right are swapped, though up and down are not), and exactly the same size as the object; additionally, the image sits as far behind the mirror as the object sits in front of it. A useful practical consequence: the minimum-height mirror needed for a person of height to see the whole of themselves is only , independent of how far they stand from the mirror -- derived by noting the normals at the two extreme points of reflection (for rays from the head and from the feet) each bisect the corresponding angle between incident and reflected ray, so only half the person's own height in mirror surface is actually used. If an object is placed between two plane mirrors inclined at angle to each other, the number of images formed is when works out to be an even integer (for any placement o …
Worked out. A person of total height h stands facing a vertical plane mirror, with eyes at E between the head H and the feet F, at heights h1 above and h2 below eye level respectively (h = h1 + h2). Light leaving the head must reflect off the mirror and reach the eyes, and separately light leaving the feet must also reflect off the mirror and reach the eyes; applying the law of reflection to both rays shows the normals at the two points of reflection exactly bisect the angles between each incident ray and its corresponding reflected ray. Working through the resulting geometry shows the vertical span of mirror actually used is only h1/2 (for the head ray) plus h2/2 (for the feet ray), giving a total required mirror height of (h1+h2)/2 = h/2 -- so a person needs a mirror only half their own height to see the whole of themselves, and (perhaps counter-intuitively) this minimum height …