Physics 212 Lecture 27, Slide 1 Physics 212 Lecture 27: Mirrors

Main Point 1 First, we determined that both the mirror equation, the equation that relates the image distance to the object distance for a single mirror, and the magnification equation that relates the image size to object size, are identical to the corresponding equations for lenses, provided we adopt the following conventions. Concave mirrors have positive focal lengths while convex mirrors have negative focal lengths. Image distances are positive if the image is real, when the image is located in front of the mirror. Image distances are negative if the image is virtual, when the image is located behind the mirror. Physics 212 Lecture 27, Slide 2

Main Point 2 Second, we determined that these equations also hold for plane mirrors if we define the focal length of a plane mirror to be infinity. Physics 212 Lecture 27, Slide 3

Main Point 3 Third, we determined that, in the small angle approximation, the focal length of a concave spherical mirror is one half the radius of curvature of the mirror. Physics 212 Lecture 27, Slide 4

Physics 212 Lecture 27, Slide 5 Reflection ii rr That’s all of the physics – everything else is just geometry! Angle of incidence = Angle of reflection  i =  r

Physics 212 Lecture 27, Slide 6 Flat Mirror All you see is what reaches your eyes –You think object’s location is where rays appear to come from. rr ii Flat Mirror Object 12

Physics 212 Lecture 27, Slide 7 If she stands closer to the mirror, what will be the lowest part of her reflection she can see in the mirror. A. Above her knee B. Her knee C. Below her knee A woman is looking at her reflection in a flat vertical mirror. The lowest part of her body she can see is her knee. ACTCD

Physics 212 Lecture 27, Slide 8 Checkpoint 1a The diagram above shows three light rays reflected off a concave mirror. Which ray is NOT correct? ABC C is not correct as it does not go through the focal point.

Physics 212 Lecture 27, Slide 9 Checkpoint 1b The diagram above shows three light rays reflected off a concave mirror. The image is A. Upright and reducedB. Upright and enlarged C. Inverted and reducedD. Inverted and enlarged

Physics 212 Lecture 27, Slide 10

Physics 212 Lecture 27, Slide 11 Checkpoint 2a If the object is behind the focal length it will reflect an inverted image. If the object is in front of the focal length it will produce a virtual upright image. The image produced by a concave mirror of a real object is A. Always upright B. Always invertedC. Sometimes upright and sometimes inverted

Physics 212 Lecture 27, Slide 12 Checkpoint 2b It's like the back of a spoon, or one of those mirrors in the corner of a convenience store. The image produced by a convex mirror of a real object is A. Always upright B. Always invertedC. Sometimes upright and sometimes inverted

Physics 212 Lecture 27, Slide 13

Physics 212 Lecture 27, Slide 14 Concave: Consider the case where the shape of the mirror is such that light rays parallel to the axis of the mirror are all “focused” to a common spot a distance f in front of the mirror: f These mirrors are often sections of spheres (assumed in this class). For such “spherical” mirrors, we assume all angles are small even though we draw them big to make it easy to see… Concave mirrors

Physics 212 Lecture 27, Slide 15 object 1) Draw ray parallel to axis reflection goes through focus 2) Draw ray through focus reflection is parallel to axis image You now know the position of the same point on the image Recipe for finding image: 2f f

Physics 212 Lecture 27, Slide 16 Convex: Consider the case where the shape of the mirror is such that light rays parallel to the axis of the mirror are all “focused” to a common spot a distance f behind the mirror: f Convex Mirrors

Physics 212 Lecture 27, Slide 17

Physics 212 Lecture 27, Slide 18 object image(virtual) S>0 S’<0 f<0 S > 0

Physics 212 Lecture 27, Slide 19 Executive Summary - Mirrors: 2f > S > f realinvertedbigger f > S > 0 virtualuprightbigger S > 0 virtualuprightsmaller f concave (converging) f convex (diverging) S > 2f realinvertedsmaller

Physics 212 Lecture 27, Slide 20 It’s always the same: You just have to keep the signs straight: Lens sign conventions S: positive if object is “upstream” of lens S’ : positive if image is “downstream” of lens f: positive if converging lens Mirrors sign conventions S: positive if object is “upstream” of mirror S’ : positive if image is “upstream” of mirror f: positive if converging mirror (concave)

Physics 212 Lecture 27, Slide 21 R=50 y x An arrow is located in front of a convex spherical mirror of radius R = 50cm. The tip of the arrow is located at (-20cm,-15cm). Where is the tip of the arrow’s image? Conceptual Analysis Strategic Analysis (-20,-15) Calculation

Physics 212 Lecture 27, Slide 22

Physics 212 Lecture 27, Slide 23