Real Images vs Virtual Images Real vs Virtual

Real Images vs. Virtual Images

Real vs. Virtual Images Real images are formed by mirrors or lenses when light rays actually converge and pass through the image. Real images will be located in front of the mirror forming them. A real image can be projected onto a piece of paper or a screen. If photographic film were placed here, a photo could be created. Virtual images occur where light rays only appear to have originated. For example, sometimes rays appear to be coming from a point behind the mirror. Virtual images can’t be projected on paper, screens, or film since the light rays do not really converge there. Examples are forthcoming.

Plane Mirror Rays emanating from an object at point P strike the mirror and are reflected with equal angles of incidence and reflection. After reflection, the rays continue to spread. If we extend the rays backward behind the mirror, they will intersect at point P’, which is the image of point P. To an observer, the rays appear to come from point P’, but no source is there and no rays actually converging there. For that reason, this image at P’ is a virtual image. The image, I, formed by a plane mirror of an object, O, appears to be a distance di , behind the mirror, equal to the object distance do. Animation Object P P’ Virtual Image do O di I Continued…

Plane Mirror (cont. ) Two rays from object P strike the mirror at points B and M. Each ray is reflected such that i = r. Triangles BPM and BP’M are congruent by ASA (show this), which implies that do= di and h = h’. Thus, the image is the same distance behind the mirror as the object is in front of it, and the image is the same size as the object image P h do B M di P’ h’ Image Object Mirror With plane mirrors, the image is reversed left to right (or the front and back of an image ). When you raise your left hand in front of a mirror, your image raises its right hand. Why aren’t top and bottom reversed?

Concave and Convex Mirrors Concave and convex mirrors are curved mirrors similar to portions of a sphere. light rays Concave mirrors reflect light from their inner surface, like the inside of a spoon. light rays Convex mirrors reflect light from their outer surface, like the outside of a spoon.

Concave Mirrors • Concave mirrors are approximately spherical and have a principal axis that goes through the center, C, of the imagined sphere and ends at the point at the center of the mirror, A. The principal axis is perpendicular to the surface of the mirror at A. • CA is the radius of the sphere, or the radius of curvature of the mirror, R. • Halfway between C and A is the focal point of the mirror, F. This is the point where rays parallel to the principal axis will converge when reflected off the mirror. • The length of FA is the focal length, f. • The focal length is half of the radius of the sphere (proven on next slide).

r = 2 f l nt ge tan To prove that the radius of curvature of a concave mirror is twice its focal length, first construct a tangent line at the point of incidence. The normal is perpendicular to the tangent and goes through the center, C. Here, i = r = . By alt. int. angles the angle at C is also , and α = 2 β. s is the arc length from the principle axis to the pt. of incidence. Now imagine a sphere centered at F with radius f. If the incident ray is close to the principle axis, s the arc length of the new sphere is about the same as s. From s = r , we have s = r β and • C • F f s f α = 2 f β. Thus, r β 2 f β, and r = 2 f. r ine

Focusing Light with Concave Mirrors Light rays parallel to the principal axis will be reflected through the focus (disregarding spherical aberration, explained on next slide. ) In reverse, light rays passing through the focus will be reflected parallel to the principal axis, as in a flood light. Concave mirrors can form both real and virtual images, depending on where the object is located, as will be shown in upcoming slides.