2 Types of Images for Mirrors and Lenses A real image is one in which light actually passes through the image pointReal images can be displayed on screensA virtual image is one in which the light does not pass through the image pointVirtual images cannot be displayed on screens
3 The object distance is the distance from the object to the mirror or lens Denoted by pThe image distance is the distance from the image to the mirror or lensDenoted by qThe lateral magnification of the mirror or lens is the ratio of the image height to the object heightDenoted by MFlat Mirror
4 QUICK QUIZ 23.1In the overhead view of the figure below, the image of the stone seen by observer 1 is at C. Where does observer 2 see the image––at A, at B, at C, at D, at E, or not at all?
6 Concave Mirror The mirror has a radius of curvature of R Its center of curvature is the point CPoint V is the center of the spherical segmentA line drawn from C to V is called the principle axis of the mirror
7 Image Formed by a Concave Mirror Geometry shows the relationship between the image and object distance isMagnification ish’ is negative when the image is inverted with respect to the object
11 Convex MirrorsA convex mirror is also called a diverging mirror
12 Ray DiagramRay 1 is drawn parallel to the principle axis and is reflected back through the focal point, FRay 2 is drawn through the focal point and is reflected parallel to the principle axisRay 3 is drawn through the center of curvature and is reflected back on itself
17 True or false?(a) The image of an object placed in front of a concave mirror is always upright. (b) The height of the image of an object placed in front of a concave mirror must be smaller than or equal to the height of the object. (c) The image of an object placed in front of a convex mirror is always upright and smaller than the object.
18 Problem 17A child holds a candy bar 10.0 cm in front of a convex mirror and notices that the image is only one-half the size of the candy bar. What is the radius of curvature of the mirror?
19 Images Formed by Refraction When n2 > n1,Object distance, image distance and radius of curvature are related by the equation:Real images are formed on the side opposite from the objectSign conventions – Table 23.2
21 Flat Refracting Surface The image and the object are on the same side of the surface. The image is virtual
22 QUICK QUIZ 23.2A person spear fishing from a boat sees a fish located 3 m from the boat at an apparent depth of 1 m. To spear the fish, should the person aimat,(b) above, or(c) below the image of the fish?
23 Problem 53A parallel beam of light enters a glass hemisphere perpendicular to the flat face, as shown in Figure P The radius is R = 6.00 cm, and the index of refraction is n = Determine the point at which the beam is focused. (Assume paraxial rays; that is, all rays are located close to the principal axis.)
24 Conceptual question10. Why does a clear stream appear to be shallower than it actually is?
25 Atmospheric Refraction and Mirages A mirage can be observed when the air above the ground is warmer than the air at higher elevationsThe rays in path B are directed toward the ground and then bent by refractionThe observer sees both an upright and an inverted image
26 Thin Lens Shapes These are examples of converging lenses They have positive focal lengthsThey are thickest in the middle
27 Thin Diverging Lenses These are examples of diverging lenses They have negative focal lengthsThey are thickest at the edges
28 Lens EquationsThe geometric derivation of the equations is very similar to that of mirrors
29 Sign Conventions for Thin Lenses QuantityPositive WhenNegative WhenObject location (p)Object is in front of the lensObject is in back of the lensImage location (q)Image is in back of the lensImage is in front of the lensImage height (h’)Image is uprightImage is invertedR1 and R2Center of curvature is in back of the lensCenter of curvature is in front of the lensFocal length (f)Converging lensDiverging lens
31 Ray Diagrams for Thin Lenses The first ray is drawn parallel to the first principle axis and then passes through (or appears to come from) one of the focal lengthsThe second ray is drawn through the center of the lens and continues in a straight lineThe third ray is drawn from the other focal point and emerges from the lens parallel to the principle axis
32 Ray Diagram for Converging Lens, p > f The image is realThe image is inverted
33 Ray Diagram for Converging Lens, p < f The image is virtualThe image is upright
34 Ray Diagram for Diverging Lens The image is virtualThe image is upright
35 Conceptual questions5. You are taking a picture of yourself with a camera that uses an ultrasonic range finder to measure the distance to the object. When you take a picture of yourself in a mirror with this camera, your image is out of focus. Why?14. Lenses used in sunglasses whether converging or diverging, are always designed such that the middle of the lens curves away from the eye. Why?
36 QUICK QUIZ 23.4A plastic sandwich bag filled with water can act as a crude converging lens in air. If the bag is filled with air and placed under water, is the effective lens (a) converging or (b) diverging?
37 QUICK QUIZ 23.6An object is placed to the left of a converging lens. Which of the following statements are true and which are false? (a) The image is always to the right of the lens. (b) The image can be upright or inverted. (c) The image is always smaller or the same size as the object.
39 Problem 44. Two converging lenses having focal lengths of 10 Problem 44. Two converging lenses having focal lengths of 10.0 cm and 20.0 cm are placed 50.0 cm apart, as shown in Figure. The final image is to be located between the lenses, at the position indicated. (a) How far to the left of the first lens should the object be positioned? (b) What is the overall magnification? (c) Is the final image upright or inverted?
40 Problem 61The lens maker’s equation for a lens with index n1 immersed in a medium with index n2 takes the form1/f=(n1/n2-1)(1/R1-1/R2)A thin diverging glass lens (index = 1.50) with R1 = –3.00 m and R2 = –6.00 m is surrounded by air. An arrow is placed 10.0 m to the left of the lens.Determine the position of the image.Repeat with the arrow and lens immersed inwater (index = 1.33);(c) a medium with an index of refraction of 2.00.
41 Spherical AberrationResults from the focal points of light rays far from the principle axis are different from the focal points of rays passing near the axisFor a mirror, parabolic shapes can be used to correct for spherical aberration
42 Chromatic AberrationDifferent wavelengths of light refracted by by a lens focus at different pointsViolet rays are refracted more than red raysThe focal length for red light is greater than the focal length for violet lightChromatic aberration can be minimized by the use of a combination of converging and diverging lenses
43 Conceptual questionsQuestion 4. Explain why a mirror cannot give rise to chromatic aberration.Question 15. Why does a focal length of a mirror not depend on the mirror material when the focal length of a lens depends on the lens material?
46 True or false?(a) The image of an object placed in front of a concave mirror is always upright. (b) The height of the image of an object placed in front of a concave mirror must be smaller than or equal to the height of the object. (c) The image of an object placed in front of a convex mirror is always upright and smaller than the object.
47 Review questions 1. What is the focal length of a flat mirror? a. 0 positiveinfiniteNegative2. The magnification of a 3 cm object placed 5 cm from a certain lens is -1. What is the focal distance of the lens?0.4 cm0.5 cm2.5 cm5.0 cm
48 3. Which of the following is responsible for mirage? a. diffraction b. reflectionc. refractiond. dispersion4. An alligator sits 1 m below the surface of water of index of refraction n=1.4. The alligator’s view of objects above the surface is restricted to a circular window at the surface of radiusa m b. 1 mc m d. 2.6 m