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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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**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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**17. 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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**Right angle mirror system**

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**Check Your Understanding**

If a toddler crawls towards a mirror at a rate of 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**

do - the distance from the mirror to the object di - 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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**17. Ray Tracing and the Mirror Equation**

Here are the sign conventions for concave and convex mirrors:

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