P06 ray diagrams with concave mirrors and intro to problem solving.notebook

Transcription

1 Ray Diagrams Concave Mirror A concave mirror is a converging mirror because parallel rays will. For any object, millions and millions of rays are reflected in all directions. Some of these rays hit the mirror and are reflected. All of these reflected rays obey the law of reflection that is the angle of will be the equal to the. Because these reflected rays are altered an image will be created. If the reflected rays reunite at one location the image is said to be. If the reflected rays are diverging, then our brain will trace them back to the place where we thought they originated called a image. Students can draw several rays, measure the angle of incidence and the angle of reflection for each ray to find where at least 2 reflected rays intersect OR students can trace 3 special incident rays whose reflected rays can be determined without measuring an angle. 3 Special Incident Rays 1. An incident ray which is traveling parallel to the principal axis will reflect 2. An incident ray which travels through the focal point will reflect 3. An incident ray that travels through the centre of curvature or travels as if it passed through the centre of curvature will reflect. Note 1 only 2 rays need to be drawn to find the location of the image. When drawing 3 incident rays, if the rays aren't carefully drawn, or if the mirror is not perfect (spherical aberration), then the 3 rays will not meet at exactly the same spot. 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 ( ) 1

2 For eacf the following, find the image and state the characteristics of the image. What pattern exists with the images as you move the object closer and closer to the mirror? 2

3 What pattern exists as the object moves closer to the focal point? What pattern exists in the last two diagrams? 3

4 Summary of Results for a Concave Mirror Objects placeut of F (whose distance to the vertex is greater than the focal length) will produce images. All real images are When the object is far from the mirror, the image is close to and the image size is As the object moves closer to the mirror, the image and the size of the image When the object is placed at C, the image appears at and it is the size. As the object moves inside C, approaching F, the image forms away and the size of the image is than the actual object. At F, image forms since the reflected rays are When the object is between F and V, the reflected rays. Since our eye believes that light travels in a straight line, our brain takes these diverging rays back to the place where we think they meet, behind the. We say this image is because the rays don't really go behind the mirror. * Remember that all rays drawn behind the mirror should be dotted because light does no really travel behind the mirror. 4

5 The Magnification Equation and the Mirror Equation Scientists often collect data to look for patterns in the result. By completing the following table, definite relationships will emerge. object hi d i Measurements from Ray Diagrams for a Concave Mirror h i d i f (cm) (cm) (cm) (cm) (cm) d i h i (cm 1 ) (cm 1 ) d i f 5

6 Derived Equations From this analysis, two unique equations emerge. The Magnification Equation The Mirror Equation M = d i h i = d i = 1 f Sign convention. To deal with the different types of images, the following sign convention is used. inverted images have a negative height virtual images have a negative distance to the image diverging mirrors (Convex mirrors) have a negative focal length. Use the two equations to answer the following word problems. 1. A concave mirror has a focal lengtf 6.0 cm. 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 concave mirror has a focal lengtf 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 lengtf 3.0 cm. An object with a height of 3.0 cm is placed 8.0 cm in front of the mirror. a) Calculate the image distance. b) Calculate the image height. 4. A member of "Pippin" is applying make up using a concave mirror. The actor's face is 35 cm in front of the mirror and the image is 72 cm behind the mirror (virtual). a) What is the magnification of the mirror? b) Use the mirror equation to determine the focal lengtf the mirror. (do not forget about the sign convention. 5. A concave mirror magnifies an object placed 30.0 cm from the mirror by a factor of Calculate the radius of curvature of the mirror. 6