A light beam striking a boundary between two media can be partly transmitted and partly reflected at the boundary.

The ratio of the light reflected from a surface to the light falling on the surface is called reflectance.

Reflection where scattering of the reflected rays is negligible is regular reflection.

Specular (polished) surfaces cause regular reflection Specular (polished) surfaces cause regular reflection. Irregular surfaces produce scattering, or diffusion of light.

Without this diffusion shaded areas would be almost totally dark and sunlit areas would be unbearably bright.

First law of reflection - the angle of incidence is equal to the angle of reflection.

Normal - a line perpendicular to the reflecting surface Normal - a line perpendicular to the reflecting surface. Angle of incidence - angle between the incident ray and the normal. Angle of reflection - angle between the reflected ray and the normal.

Rene Descartes discovered the “Law of Reflection” (or maybe it was Euclid)

Second law of reflection - the incident ray, the reflected ray, and the normal all lie in the same plane.

Virtual image - rays that appear to diverge from the image point do not actually pass through that point.(erect, larger or smaller, cannot be projected on a screen)

Plane mirrors produce images that are virtual, erect, same size; right and left are interchanged.

Concave mirror – a spherical mirror shaped like the inside of a sphere.

Convex mirror – a spherical mirror shaped like the outside of a sphere.

Real image - image formed by converging rays of light actually passing through the image point. (inverted, larger or smaller)

Center of curvature, C, is the center of the original sphere Center of curvature, C, is the center of the original sphere. Vertex, V, is the center of the mirror. Principle axis of the mirror is the line drawn through C and V.

Secondary axis is any other line drawn through C to the mirror Secondary axis is any other line drawn through C to the mirror. Normal is a radius from the point of incidence of a light ray. Principle focus is the point on the PA where light rays close to and parallel to the PA converge.

Focal length, f, is the distance from the vertex to the principle focus. Aperture determines the amount of light intercepted by the mirror.

Concave mirrors are called converging mirrors Concave mirrors are called converging mirrors. Convex mirrors are called diverging mirrors.

Focal length is one half the radius of curvature.

Parallel rays parallel to the PA converge at the principle focus Parallel rays parallel to the PA converge at the principle focus. Parallel rays that are not parallel to the PA converge at a point in a plane which is perpendicular to the PA.

Mirrors with a large aperture focus parallel rays near the edge of the mirror at points nearer the mirror than the principle focus. This is called spherical aberration and results in fuzzy images.

Parabolic mirrors correct spherical aberration.

The image formed in a curved mirror can be produced by ray tracing.

It is convenient to produce three rays that leave the same point on an object: Ray 1 is parallel to the principle axis and reflects through the focal point, Ray 2 passes through the focal point and reflects parallel to the principle axis, Ray 3 travels through the center of curvature and thus reflects back on itself.

Images formed by concave mirror: Case #1 Object at an infinite distance.

Case #2 Object at a finite distance beyond the center of curvature

Case #3 Object at center of curvature

Case #4 Object between the center of curvature and principle focus

Case #5 Object at principle focus

Case #6 Object between principle focus and mirror

Convex mirrors

Convex mirrors

Mirror equations: 1/f = 1/do + 1/di hi / ho = di / do

1. The numerical value of the focal length f of a concave mirror is positive. 2. The numerical value of the focal length f of a convex mirror is negative. 3. The numerical value of the real object distance do is positive.

4. The numerical value of the real image distance di is positive. 5 4. The numerical value of the real image distance di is positive. 5. The numerical value of the virtual image distance di is negative.

Ex. 3 - A 2. 0-cm-high object is placed 7 Ex. 3 - A 2.0-cm-high object is placed 7.10 cm from a concave mirror whose radius of curvature is 10.20 cm. Find (a) the location of the image and (b) its size.

Ex. 4 - An object is placed 6.00 cm in front of a concave mirror that has a 10.0-cm focal length. (a) Determine the location of the image. (b) If the object is 1.2 cm high, find the image height.

Ex. 5 - A convex mirror is used to reflect light from an object placed 66 cm in front of the mirror. The focal length of the mirror is f = -46 cm. Find (a) the location of the image and (b) the magnification.

Ex. 6 - An object is placed 9. 00 cm in front of a mirror Ex. 6 - An object is placed 9.00 cm in front of a mirror. The image is 3.00 cm closer to the mirror when the mirror is convex than when it is planar. Find the focal length of the convex mirror.