1. Announcements Two exams down, one to go! No HW this week. Office hours: My office hours today from 2-3 pm (or make an appointment) Always check out http://www.phys.ufl.edu/courses/phy2054/spring11/ for more announcementshttp://www.phys.ufl.edu/courses/phy2054/spring11/ QUESTIONS? PLEASE ASK!

2. Chapter 23 Mirrors and Lenses LIGO mirror Credit: LIGO Laboratory, Caltech James Webb Space Telescope Credit: NASA LIGO mirror Credit: LIGO Laboratory, Caltech http://www.ubergizmo.com/15/archives/2010/ 09/diy_macro_lens_for_your_nexus_one.html

3. Images and Mirrors Definitions object distance p - distance from the object to the mirror, lens image distance q - distance from the image to the mirror, lens lateral magnification M - ratio of the image height to the object height Images are formed at the point where The rays of light actually intersect ( ‘ real image ’ ) The rays of light appear to originate ( ‘ virtual image ’ ) To find where an image is formed, it is always necessary to follow at least two rays of light as they reflect from the mirror

4. Types of Images for Mirrors and Lenses A real image is one in which light actually passes through the image point Real images can be displayed on screens A virtual image is one in which the light does not pass through the image point The light appears to diverge from that point Virtual images cannot be displayed on screens When you look in a flat mirror, you see a virtual image Real Image Virtual Image

5. Magnification The lateral magnification is defined as Magnification doesn ’ t always mean enlargement The image can be smaller than the object (sometimes called de- magnification)

6. Flat Mirrors One ray starts at P, follows path PQ and reflects back on itself A second ray follows path PR and reflects according to the Law of Reflection Both rays appear to come from a single point behind the mirror The image is as far behind the mirror as the object is in front p = |q| The image is unmagnified The image height is the same as the object height h ’ = h and M = 1  The image …  … is virtual  … is upright  … has the same orientation as the object  There is an apparent left-right reversal in the image

7. Concave Spherical Mirrors A spherical mirror has the shape of a segment of a sphere concave spherical mirror - mirror surface on the inner (concave) side of the curve The mirror has a radius of curvature of R center of curvature is the point C Point V is the center of the spherical segment A line drawn from C to V is called the principle axis of the mirror

8.  Geometry can be used to determine the magnification of the image  h ’ is negative when the image is inverted with respect to the object Concave Mirror, Image A point source of light placed at O Rays drawn from O; after reflecting from the mirror, rays converge at point I Point I is called the image point Light actually passes through the point so the image is real

9. Image Formed by a Concave Mirror Relationship between image and object distances mirror equation If an object is very far away, then p= and 1/p = 0 Incoming rays are essentially parallel In this special case, the image point is called the focal point

10. Focal Point and Focal Length, cont The distance from the mirror to the focal point is called the focal length The focal length is ½ the radius of curvature The focal point is dependent solely on the curvature of the mirror, not by the location of the object f = R / 2 The mirror equation can be expressed as

11. Problem 23.47, p 787 An object placed 10.0 cm from a concave spherical mirror produces a real image 8.00 cm away from the mirror. If the object is moved to a new position 20.0 cm from the mirror, what is the position of the image? Is the final image real or virtual?

12. Convex Mirrors Rays from any point on the object diverge after reflection as though they were coming from a point behind the mirror Image is virtual - lies behind the mirror at the point where the reflected rays appear to originate In general, the image formed by a convex mirror is upright, virtual, and smaller than the object

13. Sign Conventions for Mirrors

14. Ray Diagram for Concave Mirror, p > R The object is outside the center of curvature of the mirror The image is real The image is inverted The image is smaller than the object

15. Ray Diagram for a Concave Mirror, p < f The object is between the mirror and the focal point The image is virtual The image is upright The image is larger than the object

16. Ray Diagram for a Convex Mirror The object is in front of a convex mirror The image is virtual The image is upright The image is smaller than the object

17. Images Formed by Refraction Rays originate from the object point, O, and pass through the image point, I When n 2 > n 1, Real images are formed on the side opposite from the object

18. Flat Refracting Surface The image formed by a flat refracting surface is on the same side of the surface as the object The image is virtual The image forms between the object and the surface The rays bend away from the normal since n 1 > n 2

19. Atmospheric Refraction and Mirages A mirage can be observed when the air above the ground is warmer than the air at higher elevations The rays in path B are directed toward the ground and then bent by refraction Related to total internal reflection – n is smaller near the ground The observer sees both an upright and an inverted image

20. Answer to 23.47