Chapter 34A - Reflection and Mirrors (Geometrical) A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University © 2007 Objectives: After completing this module, you should be able to: • Explain and discuss with diagrams, reflection, absorption, and refraction of light rays. • Illustrate graphically the reflection of light from plane, convex, and concave mirrors. • Define and illustrate your understanding of real, virtual, erect, inverted, enlarged, and diminished as applied to images. • Use geometrical optics to draw images of an object at various distances from converging and diverging mirrors. Geometrical Optics In the study of how light behaves, it is useful to use “light rays” and the fact that light travels in straight lines. When light strikes the boundary between two media, three things may happen: reflection, refraction, or absorption. Air absorption reflection Water refraction Reflection, Refraction, and Absorption Air Reflection: A ray from air strikes the water and returns to the air. Refraction: A ray bends into the water toward the normal line. absorption reflection Water refraction Absorption: A ray is absorbed atomically by the water and does not reappear. The Laws of Reflection 1. The angle of incidence qi is equal to the angle of reflection qr : Air N reflection qi qr Water qi = qr All ray angles are measured with respect to normal N. 2. The incident ray, the reflected ray, and the normal N all lie in the same plane. 3. The rays are completely reversible. The Plane Mirror A mirror is a highly polished surface that forms images by uniformly reflected light. Note: images appear to be equi-distant behind mirror and are rightleft reversed. Definitions Object distance: The straight-line distance p from the surface of a mirror to the object. Image distance: The straight-line distance q from the surface of a mirror to the image. Object distance = Image distance Object Image p=q qi = qr p q Real and Virtual Real images and objects are formed by actual rays of light. (Real images can be projected on a screen.) Virtual images and objects do not really exist, but only seem to be at a location. Light rays Real object No light Virtual image Virtual images are on the opposite side of the mirror from the incoming rays. Image of a Point Object Plane mirror q=p Real object p q Virtual image Image appears to be at same distance behind mirror regardless of viewing angle. Image of an Extended Object Plane mirror q=p p q Virtual image Image of bottom and top of guitar shows forward-back, right-left reversals. Terms for Spherical Mirrors A spherical mirror is formed by the inside (concave) or outside (convex) surfaces of a sphere. A concave spherical mirror is shown here with parts identified. The axis and linear aperture are shown. Concave Mirror R V Axis C Linear aperture Center of Curvature C Radius of curvature R Vertex V The Focal Length f of a Mirror Incident parallel ray C R F qi qr axis Focal point The focal length, f V f Since qi = qr, we find that F is midway between V and C; we find: The focal length f is: R f 2 The focal length f is equal to half the radius R The Focus of a Concave Mirror The focal point F for a concave mirror is the point at which all parallel light rays converge. F For objects located at infinity, the real image appears at the focal point since rays of light are almost parallel. Focal point R f 2 Incident parallel Rays axis C The Focus of a Convex Mirror The focal point for a convex mirror is the point F from which all parallel light rays diverge. Virtual focus; reflected rays diverge. Incident Rays R C R f 2 F axis Reflected Rays Image Construction: Ray 1: A ray parallel to mirror axis passes through the focal point of a concave mirror or appears to come from the focal point of a convex mirror. Ray 1 C F Object Concave mirror Convex mirror C F Ray 1 Object Image Construction (Cont.): Ray 2: A ray passing through the focus of a concave mirror or proceeding toward the focus of a convex mirror is reflected parallel to the mirror axis. Ray 1 C Ray 2 Convex mirror Ray 1 F Image Concave mirror Ray 2 C F Image Image Construction (Cont.): Ray 3: A ray that proceeds along a radius is always reflected back along its original path. Ray 1 Ray 3 Ray 1 Ray 2 Ray 2 C Concave mirror F C Ray 3 Convex mirror F Image The Nature of Images An object is placed in front of a concave mirror. It is useful to trace the images as the object moves ever closer to the vertex of the mirror. We will want to locate the image and answer three questions for the possible positions: 1. Is the image erect or inverted? 2. Is the image real or virtual? 3. Is it enlarged, diminished, or the same size? Object Outside Center C 1. The image is inverted; i.e., opposite of the object orientation. 2. The image is real; i.e., formed by actual light rays in front of mirror. 3. The image is diminished in size; i.e., smaller than the object. Ray 1 Ray 2 C Concave mirror F Ray 3 Image is located between C and F Object at the Center C 1. The image is inverted; i.e., opposite of the object orientation. 2. The image is real; i.e., formed by actual light rays in front of mirror. 3. The image is the same size as the object. Ray 1 Ray 2 C F Ray 3 Image is located at C, inverted. Object Between C and F 1. The image is inverted; i.e., opposite of the object orientation. 2. The image is real; i.e., formed by actual light rays in front of mirror. 3. The image is enlarged in size; i.e., larger than the object. Ray 1 Ray 3 C F Ray 2 Image is outside of the center C Object at Focal Point When the object is located at the focal point of the mirror, the image is not formed (or it is located at infinity). The parallel reflected rays never cross. Ray 3 Ray 1 C F Reflected rays are parallel Image is located at infinity (not formed). Object Inside Focal Point 1. The image is erect; i.e., same orientation as the object. 2. The image is virtual; that is, it seems to be located behind mirror. 3. The image is enlarged; bigger than the object. C F Erect and enlarged Virtual image Image is located behind the mirror Observe the Images as Object Moves Closer to Mirror C Ray Ray 1 1 Ray 11 Ray 2 Ray 2 Ray Ray 3 C C C C FF F F Virtual Rayrays 3image Erect and Reflected Concave Ray Ray 3 2 enlarged are parallel mirror Convex Mirror Imaging Convex mirror Ray 1 Convex mirror Ray 1 2 Ray 2 C F Image C F Image gets larger as object gets closer All images are erect, virtual, and diminished. Images get larger as object approaches. Converging and Diverging Mirrors Concave mirrors and converging parallel rays will be called converging mirrors from this point onward. Converging Mirror C Convex mirrors and diverging parallel rays will be called diverging mirrors from this point onward. Diverging Mirror F C Concave F Convex Summary Reflection: A ray from air strikes the water and returns to the air. Air absorption reflection Water refraction Refraction: A ray bends into the water toward the normal line. Absorption: A ray is absorbed atomically by the water and does not reappear. Summary (Cont.) 1. The angle of incidence qi is equal to the angle of reflection qr : Air N reflection qi qr Water qi = qr All ray angles are measured with respect to normal N. 2. The incident ray, the reflected ray, and the normal N all lie in the same plane. 3. The rays are completely reversible. Summary (Definitions) Object distance: The straight-line distance p from the surface of a mirror to the object. Image distance: The straight-line distance q from the surface of a mirror to the image. Real image: An image formed by real light rays that can be projected on a screen. Virtual image: An image that appears to be at a location where no light rays reach. Converging and diverging mirrors: Refer to the reflection of parallel rays from surface of mirror. Image Construction Summary: Ray 1: A ray parallel to mirror axis passes through the focal point of a concave mirror or appears to come from the focal point of a convex mirror. Ray 2: A ray passing through the focus of a concave mirror or proceeding toward the focus of a convex mirror is reflected parallel to mirror axis. Ray 3: A ray that proceeds along a radius is always reflected back along its original path. Summary (Cont.) For plane mirrors, the object distance equals the image distance and all images are erect and virtual. For converging mirrors and diverging mirrors, the focal length is equal to one-half the radius. All images formed from convex mirrors are erect, virtual, and diminished in size. Except for objects located inside the focus (which are erect and virtual), all images formed by converging mirrors are real and inverted. CONCLUSION: Chapter 34A Reflection and Mirrors (Geometrical)