The Law of Reflection

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1 The Law of Reflection In the diagram, the ray of light approaching the mirror is known as the incident ray (labeled I in the diagram). The ray of light which leaves the mirror is known as the reflected ray (labeled R in the diagram). At the point of incidence where the ray strikes the mirror, a line can be drawn perpendicular to the surface of the mirror; this line is known as a normal line (labeled N in the diagram). The normal line divides the angle between the incident ray and the reflected ray into two equal angles. The angle between the incident ray and the normal is known as the angle of incidence. The angle between the reflected ray and the normal is known as the angle of reflection. The law of reflection states that when a ray of light reflects off a surface, the angle of incidence is equal to the angle of reflection. The diagram below illustrates the law of reflection. In order to see the image of an object in a mirror, you must look at the image of that object; when you look at the image, light will come to your eye along that line of sight. The reflection of an object can be seen from several different locations since the image point is fixed the angle of incidence and reflection changes each time you change your position.

2 The Anatomy of a Curved Mirror Spherical mirrors can be thought of as a portion of a sphere which was sliced away and then silvered on one of the sides to form a reflecting surface. Concave mirrors: were silvered on the inside of the sphere. Convex mirrors: were silvered on the outside of the sphere. In order to understand spherical mirrors, it is important to understand and learn some terminology. Principal axis: If a concave mirror is thought of as being a slice of a sphere, then there would be a line passing through the center of the sphere and attaching to the mirror in the exact center of the mirror. Center of curvature(c): The point in the center of sphere from which the mirror was sliced. Vertex (A): The point on the mirror's surface where the principal axis meets the mirror. The vertex is the geometric center of the mirror. Focal point (F): Midway between the vertex and the center of curvature Radius of curvature(r): The distance from the vertex (A) to the center of curvature (C). The radius of curvature is the radius of the sphere from which the mirror was cut. Focal length (f): Finally, the distance from the mirror to the focal point. Since the focal point is the midpoint of the line segment adjoining the vertex and the center of curvature, the focal length would be one-half the radius of curvature.

3 Real Image: When a real image is formed, it still appears to an observer as though light is diverging from the real image location. Only in the case of a real image, light is actually passing through the image location. Such images are formed on the same side of the mirror as the object and light passes through the actual image location. Virtual Image: Virtual images are images which are formed in locations where light does not actually reach. Light does not actually pass through the location on the other side of the mirror; it only appears to an observer as though the light were coming from this position. Whenever a mirror (whether a plane mirror or otherwise) creates an image which is virtual, it will be located behind the mirror where light does not really pass. Concave Mirrors Two simple rules of reflection for concave mirrors: Any incident ray traveling parallel to the principal axis on the way to the mirror will pass through the focal point upon reflection. Any incident ray passing through the focal point on the way to the mirror will travel parallel to the principal axis upon reflection. These two rules of reflection are illustrated in the diagram below.

4 Image Characteristics for Concave Mirrors The best means of summarizing this relationship is to divide the possible object locations into five general areas or points: Case 1: the object is located beyond the center of curvature (C) Case 2: the object is located at the center of curvature (C) Case 3: the object is located between the center of curvature (C) and the focal point (F) Case 4: the object is located at the focal point (F) Case 5: the object is located in front of the focal point (F) Case 1: The object is located beyond C When the object is located at a location beyond the center of curvature: The image will be somewhere between the center of curvature and the focal point. The image will be inverted. (i.e. if the object is right-side up, then the image is upside down). The image is reduced in size; in other words, the image dimensions are smaller than the object dimensions. Therefore, the magnification is a number less than 1. The image is a real image. Light rays actually converge at the image location. If a sheet of paper was placed at the image location, the actual replica of the object would appear projected upon the sheet of paper. Case 2: The object is located at C When the object is located at the center of curvature: The image will be at the center of curvature. The image will be inverted (i.e., a right-side-up object results in an upside-down image).

5 The image dimensions are equal to the object dimensions. A six-foot tall person would have an image which is six feet tall; the magnification is exactly 1. The image is real. Case 3: The object is located between C and F When the object is located in front of the center of curvature: The image will be beyond the center of curvature. The image will be inverted. The image dimensions are larger than the object dimensions. A six-foot tall person would have an image which is larger than six feet tall; the magnification is greater than 1. The image is real Case 4: The object is located at F When the object is located at the focal point: No image is formed (or the image will be at infinity). The reflected rays neither converge or diverge. After reflecting, the light rays are traveling parallel to each other and cannot produce an image. If we assume that an image is formed at infinity then: o The image will be inverted. o The image dimensions are larger than the object dimensions. o The magnification is greater than 1. o The image is a real image. Case 5: The object is located in front of F When the object is located in front of F: The image will be on the opposite side of the mirror, behind the mirror. The image will upright (not inversted). The image is enlarged; the magnification is greater than 1.

6 The image is virtual. Light rays diverge upon reflection; for this reason, the image location can only be found by extending the reflected rays backwards beyond the mirror. The point of their intersection is the virtual image location. It would appear to any observer as though light from the object were diverging from this location. Any attempt to project such an image upon a sheet of paper would fail since light does not actually pass through the image location. Summary of Different forms of image in Concave mirrors Nine different object locations are drawn and labeled with a number; the corresponding image locations are drawn in Black and labeled with the identical number. Concave mirrors can produce both real and virtual images. The Concave Mirror Equation The mirror equation expresses the quantitative relationship between the object distance (p), the image distance (q), and the focal length (f). The equation is stated as follows:

7 1 f 1 1 = + OR p q = + R p q The Magnification equation relates the ratio of the image distance and object distance to the ratio of the image height (h ) and object height (h). The magnification equation is stated as follows: q p = M=- h' h These two equations can be combined to yield information about the image distance and image height if the object distance, object height, and focal length are known. Two simple rules of reflection for convex mirrors: Convex Mirrors Any incident ray traveling parallel to the principal axis on the way to a convex mirror will reflect in a manner that its extension will pass through the focal point. Any incident ray traveling towards a convex mirror such that its extension passes through the focal point will reflect and travel parallel to the principal axis. Image Characteristics for Convex Mirrors Unlike concave mirrors, convex mirrors always produce images which share same characteristics. The location of the object does not affect the characteristics of the image. So, the characteristics of the images formed by convex mirrors are easily predictable. The diagrams are shown below. The diagrams above shows that in each case, the image is The image will be located behind the convex mirror.

8 A virtual image will be formed. Light rays diverge upon reflection; for this reason, the image location can only be found by extending the reflected rays backwards beyond the mirror. The point of their intersection is the virtual image location. It would appear to any observer as though light from the object were diverging from this location. Any attempt to project such an image upon a sheet of paper would fail since light does not actually pass through the image location. The image will be upright. The image will be smaller than the object. So, the magnification will be smaller than 1. The image is always formed between the focal point and mirror. Summary of Different forms of image in Convex mirrors The diagram below shows seven different object locations (drawn and labeled in gray) and their corresponding image locations (drawn and labeled in black). Convex mirror can only form an upright, and virtual image.

9 The Convex Mirror Equation The mirror equation expresses the quantitative relationship between the object distance (p), the image distance (q), and the focal length (f). The equation is stated as follows: = + OR = + f p q R p q (f and R are negative for convex mirror) The Magnification equation relates the ratio of the image distance and object distance to the ratio of the image height (h ) and object height (h). The magnification equation is stated as follows: q p = M=- h' h These two equations can be combined to yield information about the image distance and image height if the object distance, object height, and focal length are known.

10 Problem Solving Front, or Real side p and q positive Incident light Reflected light Back or Virtual side p and q negative No light f is always positive for concave mirror. f is always negative for convex mirror. p and q are positive if they are in front of the mirror. p and q are negative if they are in back of the mirror. p Object q Image M Magnification q h' M=h = p When M is positive, the image will be virtual, upright, and in back of the mirror. M is positive because q is negative in this situation. When M is negative, the image will be real, inverted, and in front of the mirror. M is negative because q is positive in this situation. p q or h h' M 1 p q or h h' M 1 p = q or h=h M=1

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