Chapter26[1]

# Chapter26[1] - Chapter 26 Drop a rock in a pool of water...

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Chapter 26 Drop a rock in a pool of water. What do you see? When we get far enough away from the source of the wave, it “flattens out”. We call this a PLANE WAVE. REFLECTION: In geometrical optics, we imagine light as a ray or arrow. Of course, we know that it's a wave. However, the image of a ray or an arrow helps us to work problems correctly. There are two types of reflection: 1. Specular reflection - light rays bounce off of a smooth surface like a mirror.

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2. Diffuse reflection - light rays bounce off of a rough surface and are scattered in many different directions. OK, there is a law for everything. LAW OF REFLECTION: The figure shows the geometry that we will need for most of our work in this chapter. An imaginary line is drawn perpendicular (at right angles to) the mirror or other surface that will be hit by the light ray. The ray on the left is incoming from the light source. If we measure the angle from it to the perpendicular, this is called the angle of incidence . The reflected ray of light is the one on the right and the angle from it to the perpendicular is called the angle of reflection . The law of reflection states that THE ANGLE OF INCIDENCE IS EQUAL TO THE ANGLE OF REFLECTION! THE PLANE MIRROR Standing in front of a mirror, you lift your right hand. Which hand does your image lift? 1. Image is upright, but left and right are reversed. 2. The image is located the same distance behind the mirror as the object is in front of it. 3. The image is the same size as the object.
Go over the geometry in a quick review (vertical angles, two parallel lines cut by transversal, etc). Look at the dashed blue line. This is the ray projected backward , behind the mirror that forms the image. Find y(h): Look at the right triangle formed with the person’s eye at one vertex. (green)  2 3 y tan We need to eliminate d. Look at the triangle in orange. 2d hy y tan 2 h y y d2 d 2h 3y yh  To see your entire body, how big must the mirror be?

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To see your feet, the mirror’s bottom must be halfway between your eyes and feet. To see the top of your head, the top of the mirror must be halfway between the top of your head and your eyes. So, the answer is ½ of your height. 10. • A 13.0-foot-long, nearsighted python is stretched out perpendicular to a plane mirror, admiring its reflected image. If the greatest distance to which the snake can see clearly is 27.0 ft, how close must its head be to the mirror for it to see a clear image of its tail? 2 13.0 ft 27.0 ft 2 27.0 ft 13.0 ft 14.0 ft 7.00 ft x x x   Spherical Mirrors
REMEMBER THAT THE RADIUS OF A SPHERE IS EVERYWHERE PERPENDICULAR TO ITS SURFACE! The light rays are coming in from the left. Notice that the normal (perpendicular) is the radius, which extends back to point C, called the center of curvature . If the reflected ray is extended backward, behind the mirror, they all end up at point F, called the focal point.

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Focal length for a convex mirror, R f 2 1 , where R is called the radius of curvature .
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Chapter26[1] - Chapter 26 Drop a rock in a pool of water...

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