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Reflection and Mirrors (Geometrical)

Reflection and Mirrors (Geometrical). 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.

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Reflection and Mirrors (Geometrical)

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  1. Reflection and Mirrors (Geometrical)

  2. 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.

  3. Air reflection absorption Water refraction 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.

  4. Air Air reflection reflection absorption absorption Water Water refraction refraction Reflection, Refraction, and Absorption 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: A ray is absorbed atomically by the water and does not reappear.

  5. N Air reflection qi qr Water 3. The rays are completely reversible. The Laws of Reflection 1. The angle of inci- dence qiis equal to the angle of reflection qr: 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.

  6. Note: images appear to be equi-distant behind mirror and are right-left reversed. The Plane Mirror A mirror is a highly polished surface that forms images by uniformly reflected light.

  7. Object Image Object distance Image distance = p q Definitions Object distance: The straight-line distance pfrom the surface of a mirror to the object. Image distance: The straight-line distance qfrom the surface of a mirror to the image. p = q qi = qr

  8. Light rays No light Real object Virtual image 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. Virtual images are on the opposite side of the mirror from the incoming rays.

  9. Plane mirror p q Real object Virtual image Image of a Point Object q = p Image appears to be at same distance behind mirror regardless of viewing angle.

  10. Plane mirror p q Image of an Extended Object q = p Virtual image Image of bottom and top of guitar shows forward-back, right-left reversals.

  11. Axis R V Linear aperture Terms for Spherical Mirrors A spherical mirror is formed by the inside (concave) or outside (convex) surfaces of a sphere. Concave Mirror C A concave spherical mirror is shown here with parts identified. Center of Curvature C Radius of curvature R The axis and linear aperture are shown. Vertex V

  12. Incident parallel ray qi F V C qr Focal point The focal length, f The Focal Length f of a Mirror Since qi = qr, we find that F is mid- way between Vand C; we find: R axis f The focal length f is: The focal length f is equal to half the radius R

  13. Incident parallel Rays F C axis Focal point The Focus of a Concave Mirror The focal point F for a concave mirror is the point at which all parallel light rays converge. For objects lo- cated at infinity, the real image appears at the focal point since rays of light are almost parallel.

  14. Incident Rays R axis C F Reflected Rays 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.

  15. Ray 1 Ray 1 Convex mirror C F F Object C Object Concave mirror 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.

  16. Ray 2 Convex mirror Ray 1 Ray 1 C F Image F C Image Concave mirror 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 2

  17. Ray 1 Ray 1 Ray 2 Ray 2 C F F F C C Ray 3 Concave mirror Ray 3 Convex mirror Image Image Construction (Cont.): Ray 3: A ray that proceeds along a radius is always reflected back along its original path.

  18. We will want to locate the image and answer three questions for the possible positions: 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. 1. Is the image erect or inverted? 2. Is the image real or virtual? 3. Is it enlarged, diminished, or the same size?

  19. Ray 1 Ray 2 Ray 3 Object Outside Center C 1. The image is inverted; i.e., opposite of the object orientation. C F 2. The image is real; i.e., formed by actual light rays in front of mirror. Concave mirror 3. The image is diminished in size; i.e., smaller than the object. Image is located between C and F

  20. Ray 1 Ray 3 Object at the Center C 1. The image is inverted; i.e., opposite of the object orientation. Ray 2 C F 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. Image is located at C, inverted.

  21. Ray 1 Ray 3 Ray 2 Object Between C and F 1. The image is inverted; i.e., opposite of the object orientation. C 2. The image is real; i.e., formed by actual light rays in front of mirror. F 3. The image is enlarged in size; i.e., larger than the object. Image is outside of the center C

  22. Ray 1 Ray 3 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). C F Reflected rays are parallel The parallel reflected rays never cross. Image is located at infinity (not formed).

  23. Object Inside Focal Point 1. The image is erect; i.e., same orientation as the object. C F 2. The image is virtual; that is, it seems to be located behind mirror. Virtual image Erect and enlarged 3. The image is enlarged; bigger than the object. Image is located behind the mirror

  24. Ray 1 Ray 1 Ray 1 Ray 2 Ray 3 Ray 3 C C C C C F F F F F Virtual image Reflected rays are parallel Ray 1 Erect and enlarged Concave mirror Ray 2 Ray 3 Ray 2 Ray 3 Observe the Images as Object Moves Closer to Mirror

  25. Convex mirror Ray 1 F C Convex mirror Ray 2 F C Image Convex Mirror Imaging Ray 1 2 Image gets larger as object gets closer All images are erect, virtual, and diminished. Images get larger as object approaches.

  26. Converging Mirror Diverging Mirror F C C F Convex Concave Converging and Diverging Mirrors Concave mirrors and converging parallel rays will be called converging mirrors from this point onward. Convex mirrors and diverging parallel rays will be called diverging mirrors from this point onward.

  27. Air reflection absorption Water refraction Summary 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: A ray is absorbed atomically by the water and does not reappear.

  28. N Air reflection qi qr Water 3. The rays are completely reversible. Summary (Cont.) 1. The angle of inci- dence qiis equal to the angle of reflection qr: 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.

  29. Summary (Definitions) Object distance: The straight-line distance pfrom the surface of a mirror to the object. Image distance: The straight-line distance qfrom 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.

  30. 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.

  31. 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.

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