Ray Diagrams Convex Mirror A concave mirror is a converging mirror because parallel rays will. A convex mirror is a diverging mirror because parallel rays will. Quick Activity obtain a ray box and a curved mirror. On a blank piece of paper draw the curved mirror as indicated in the diagram (1/3 of the page) Using the 3 slit option, find the principal focus on the concave side. Place the ray box on the other side of the mirror but leave the mirror in the same location. Draw the incident and reflected rays for this set up. If you traced the reflected rays back, would they meet at the same focal point? 3 Special Incident Rays 1. An incident ray which is traveling parallel to the principal axis will reflect AS IF it 2. An incident ray which travels TOWARDS the focal point will reflect 3. An incident ray that travels TOWARDS the centre of curvature will reflect. Note 1 Most students apply rule 2 incorrectly. As all the rays are drawn, it is difficult to distinguish between the incident rays and the reflected ray. So, to minimize this confusion, do not extend the incident rays behind the mirror. Also, always use dotted lines for rays drawn behind the mirror. Note 2 properly label each ray diagram before you draw any rays. Important labels include the Principal Axis (PA), Centre of Curvature ( ), Principal Focus ( ) and the Vertex ( ) Note 3 the principal focus is not a REAL principal focus in that the light rays do not travel through the focus. Due to symmetry, we still call this imaginary location, the principal focus and in the mirror equation, the focal length is assigned a value. 1
For each of the following, find the image and state the characteristics of the image. S. A. L. T. S. A. L. T. S. A. L. T. What pattern exists with the images as you move the object closer and closer to the mirror? 2
Convex Mirrors and Perception All images in a convex mirror are, and. One would think they they have no purpose if they reduce the size of the object. However, the smaller image size results from collecting light from a wider range. These mirrors are used in stores because they allow the employee to see the entire store. Our brain perceives distances through image size so when an image is smaller we think that it must be farther away when in fact the object in the mirror is than it. Young drivers are made aware of this because the passenger side mirror is a mirror. The Magnification Equation and the Mirror Equation Repeat the activity performed with a concave mirror to see if the magnification equation and the mirror equation hold true for a convex mirror for each of your three drawings. Measurements form Ray Diagrams for a Convex Mirror h o h i d i f (cm) (cm) (cm) (cm) (cm) d i h i 1 1 1 + (cm 1 ) (cm 1 ) d i f h o 3
Derived Equations http://dev.physicslab.org/document.aspx?doctype=3&filename=geometricoptics_mirrorequation.xml From this analysis, two unique equations emerge. The Magnification Equation The Mirror Equation M = d i h i = _ h o 1 1 + d i = 1 f Sign convention (for both concave and convex mirrors). To deal with the different types of images, the following sign convention is used. inverted images have a height images have a negative distance to the image diverging mirrors (Convex mirrors) have a focal length. Use the two equations to answer the following word problems. 1. A convex mirror has a focal length of 6.0 cm (negative). An object with a height of 0.60 cm is placed 10.0 cm in front of the mirror. a) Calculate the image distance. b) Calculate the image height. 2. A convex mirror has a focal length of 2.0 cm. An object with a height of 1.0 cm is placed 1.0 cm in front of the mirror. a) Calculate the image distance. b) Calculate the image height. 3. A concave mirror has a focal length of 4.0 cm. An object with a height of 4.0 cm is placed 2.0 cm in front of the mirror. a) Calculate the image distance. b) Calculate the image height. 4. The director of "Pippin" is using a convex mirror to keep an eye on the entire stage. The actor standing 4.0 m in front of the mirror has an image that appears to be 2.0 m behind the mirror (virtual). a) What is the magnification of the mirror? b) Use the mirror equation to determine the focal length of the mirror. (do not forget about the sign convention. 4
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