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REFLECTION OF LIGHT Light obeys the law of refection that states that: "The angle of incidence is equal to the angle of reflection." Angles are read from the normal. Angle of Reflection = Angle of Incidence Angles are measured with respect to the normal line Light reflection from a smooth surface is called regular or specular reflection. Light reflection from a rough or irregular surface is called diffuse reflection. FLAT MIRRORS A flat mirror reflects light rays in the same order as they approach it. Flat mirrors are made from pieces of plate glass that have been coated on the back with a reflecting material like silver or aluminum. The image is the same size as the object and the same distance behind the mirror as the object is in front of the mirror. Notice that the images formed by a flat mirror are, in truth, reflections of real objects. The images themselves are not real because no light passes through them. These images which appear to the eye to be formed by rays of light but which in truth do not exist are called virtual images. On the other hand real images are formed when rays of light actually intersect at a single point. Left-Right Reversal CURVED MIRRORS A curved mirror is a mirror that may be thought of as a portion of a reflecting sphere. If the inside of the spherical surface is the reflecting surface, the mirror is said to be concave or converging. If the outside portion is the reflecting surface, the mirror is convex or diverging. A curved mirror has a geometric center or vertex A. The center of curvature ( C )or radius R. The focal length f of the mirror is half the radius: 1 f R 2 IMAGES FORMED BY CURVED SPHERICAL MIRRORS The best method of understanding the formation of images by mirrors is through geometrical optics or ray tracing. IMAGES FORMED BY CURVED SPHERICAL MIRRORS The principal rays are: Ray 1. A ray parallel to the mirror axis passes through the focal point of a concave mirror or seems to come from the focal point of a convex mirror. Ray 2. A ray that passes through the focal point of a concave mirror or proceeds toward the focal point of a convex mirror is reflected parallel to the mirror axis. Ray 3. A ray that proceeds along a radius of the mirror is reflected back along its original path. Ray 1. A ray parallel to the mirror axis passes through the focal point of a concave mirror or seems to come from the focal point of a convex mirror. Ray 2. A ray that passes through the focal point of a concave mirror or proceeds toward the focal point of a convex mirror is reflected parallel to the mirror axis. Ray 3. A ray that proceeds along a radius of the mirror is reflected back along its original path. 9.2 a. Find the images formed by the following mirrors using the Ray Tracing method. b. Write the characteristics of each image: real or virtual, larger, smaller or same size as object and inverted or upright. VIRTUAL SAME SIZE UPRIGHT REAL SMALLER INVERTED REAL SAME SIZE INVERTED REAL LARGER INVERTED NO IMAGE IS FORMED RAYS ARE PARALLEL VIRTUAL LARGER UPRIGHT VIRTUAL SMALLER UPRIGHT REFRACTION The bending of a ray of light as it passes from one medium to another is called refraction. The speed of light c in a material is generally less than the free-space velocity of 3 x108 m/s. In water light travels about three-fourths of its velocity in air. Light travels about two-thirds as fast in glass. The ratio of the velocity c of light in a vacuum to the velocity v of light in a particular medium is called the index of refraction n for that material. c n v c = 3 x108 m/s SNELL’S LAW The ratio of the sine of the incident angle to the sine of the refracted angle is constant. n1 sinθ1 = n2 sinθ2 n1 = index of refraction of the incident medium n2 = index of refraction of the second medium THIN LENSES Lenses are an essential part of telescopes, eyeglasses, cameras, microscopes and other optical instruments. A lens is usually made of glass, or transparent plastic. The two main types of lenses are convex and concave lenses. The focal length (f) of a lens depends on its shape and its index of refraction. A converging (convex) lens is thick in the center and thin at the edges. A diverging (concave) lens is thin in the center and thick at the edges. IMAGE FORMATION BY LENSES The three principal rays are: Ray 1. A ray parallel to the axis passes through the second focal point F2 of a converging lens or appears to come from the first focal point F1 of a diverging lens. Ray 2. A ray which passes through the first focal point F1 of a converging lens or proceeds toward the second focal point F2 of a diverging lens is refracted parallel to the lens axis. Ray 3. A ray through the geometrical center of a lens will not be deviated. A real image is always formed on the side of the lens opposite to the object. A virtual image will appear to be on the same side of the lens as the object. 2. a. Find the images formed by the following lenses using the Ray Tracing method. b. Write the characteristics of each image: - real or virtual, - larger, smaller or same size as object and - upright or erect. REAL SMALLER INVERTED REAL SAME SIZE INVERTED REAL LARGER INVERTED No image is formed Rays are parallel VIRTUAL LARGER UPRIGHT VIRTUAL SMALLER UPRIGHT VIRTUAL SMALLER UPRIGHT THE MIRROR AND LENS EQUATION The mirror/lens equation can be used to locate the image: 1 1 1 d o di f Where do is the object’s distance, di is the image distance and f is the focal length. hi di M ho do The ratio M is called the magnification, ho is the object’s size and hi is the image size. R radius of curvature + converging - diverging f focal length + converging - diverging do object distance + real object + real object di image distance + real images - virtual images ho object size + if upright - if inverted hi image size + if upright - if inverted