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Chapter 17 Geometrical Optics

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Units of Chapter 17 The Reflection of Light Ray diagram for plane mirror Spherical Mirrors Ray Tracing and the Mirror Equation

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17-1 The Reflection of Light If a stone is dropped into a pond, circular waves emanate from the point where it landed. Rays, perpendicular to the wave fronts, give the direction in which the waves propagate.

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17-1 The Reflection of Light As one moves farther from a point wave source, the wave fronts become more nearly flat.

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17-1 The Reflection of Light The law of reflection states that the angle of incidence equals the angle of reflection:

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17-1 The Reflection of Light Reflection from a smooth surface is called specular reflection, in which parallel light rays are reflected in parallel. This is diffuse reflection, the scattering of light off a rough surface.

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8 Check Your Understanding A ray of light is incident towards a plane mirror at an angle of 30-degrees with the mirror surface. What will be the angle of reflection? Page 460, # 2, 3, and 5

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17. Forming Images with a Plane Mirror Light reflected from an object hits the mirror. Obeying the law of reflection, it enters the eye.

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Ray diagram for plane mirror A ray diagram is a diagram that traces the path that light takes in order for a person to view a point on the image of an object. Draw the image of the object 10

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17. Forming Images with a Plane Mirror Properties of Mirror Images Produced by Plane Mirrors: Upright, and Virtual image Left-right reversal Appears to be the same distance behind the mirror that the object is in front of the mirror. The same size as the object.

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12 Right angle mirror system 12

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13 Check Your Understanding If a toddler crawls towards a mirror at a rate of 0.25 m/s, then at what speed will the toddler and the toddler's image approach each other? A 50 cm tall dog stands 3 m from a plane mirror and looks at its image. What is the image position, height, and type? work on Ch17: Reflection packet 12

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17. Spherical Mirrors A spherical mirror has the shape of a section of a sphere. If the outside is mirrored, it is convex; if the inside is mirrored, it is concave.

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17. Spherical Mirrors Spherical mirrors have a central axis (a radius of the sphere) and a center of curvature (the center of the sphere).

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17. Spherical Mirrors Parallel rays hitting a spherical mirror come together at the focal point. A convex mirror – focal point is negative (virtual). A concave mirror – focal point is positive (real).

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17. Spherical Mirrors

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17. Ray Tracing and the Mirror Equation We use three principal rays in finding the image. The parallel ray (P ray) reflects through the focal point. The focal ray (F ray) reflects parallel to the axis. The center-of-curvature ray (C ray) reflects back along its incoming path.

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17. Ray Tracing and the Mirror Equation These three rays are illustrated here.

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17. Ray Tracing and the Mirror Equation This image shows how these three rays are used to find the image formed by a convex mirror.

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17. Ray Tracing and the Mirror Equation The process is similar for a concave mirror, although there are different results depending on where the object is placed.

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17. Ray Tracing and the Mirror Equation We derive the mirror equation using the ray diagrams:

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17. Ray Tracing and the Mirror Equation d o - the distance from the mirror to the object d i - the distance from the mirror to the image f - the focal length h - the height of the image h - the height of the object i o

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17. Ray Tracing and the Mirror Equation

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Here are the sign conventions for concave and convex mirrors:

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