3/23/ LIGO mirror Announcements LIGO mirror Two exams down, one to go! No HW this week. Credit: LIGO Laboratory, Caltech Office hours: My office hours today from 2-3 pm (or make an appointment) Chapter 23 Always check out http://www.phys.ufl.edu/courses/phy2054/spring/ for more announcements Credit: LIGO Laboratory, Caltech Mirrors and Lenses QUESTIONS? PLEASE ASK! James Webb Space Telescope Credit: NASA http://www.ubergizmo.com/5/archives/200/ 09/diy_macro_lens_for_your_nexus_one.html Types of Images for Mirrors and Lenses 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 ) Real Image A real image is one in which light actually passes through the image point A virtual image is one in which the light does not pass through the image point 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 Real images can be displayed on screens Virtual Image 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
Magnification The lateral magnification is defined as image height h' M = = object height h Magnification doest always mean enlargement The image can be smaller than the object (sometimes called demagnification) 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 = The image is virtual is upright has the same orientation as the object There is an apparent left-right reversal in the image 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 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 Geometry can be used to determine the magnification of the image M = h ' h =! q p h is negative when the image is inverted with respect to the object 2
Image Formed by a Concave Mirror Relationship between image and object distances p + q = 2 R mirror equation If an object is very far away, then p= and /p = 0 Incoming rays are essentially parallel In this special case, the image point is called the focal point 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 p + q = f Problem 23.47, p 787 An object placed 0.0 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? 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 3
Sign Conventions for Mirrors 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 Ray Diagram for a Concave Mirror, p < f Ray Diagram for a Convex Mirror 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 The object is in front of a convex mirror The image is virtual The image is upright The image is smaller than the object 4
Images Formed by Refraction Rays originate from the object point, O, and pass through the image point, I When n 2 > n, M = h ' h =! n q n 2 p Real images are formed on the side opposite from the object 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 > n 2 Atmospheric Refraction and Mirages A mirage can be observed when the air above the ground is warmer than the air at higher elevations Answer to 23.47 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 5