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Chapter 17
Geometrical Optics
Units of Chapter 17
•The Reflection of Light
• Ray diagram for plane mirror
• Spherical Mirrors
• Ray Tracing and the Mirror Equation
17-1 The Reflection of LightIf 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.
17-1 The Reflection of Light
As one moves farther from a point wave source, the wave fronts become more nearly flat.
17-1 The Reflection of Light
The law of reflection states that the angle of incidence equals the angle of reflection:
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
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
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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 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
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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.
17. Spherical Mirrors
Spherical mirrors have a central axis (a radius of the sphere) and a center of curvature (the center of the sphere).
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).
17. Spherical Mirrors
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.
17. Ray Tracing and the Mirror Equation
These three rays are illustrated here.
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.
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.
17. Ray Tracing and the Mirror Equation
We derive the mirror equation using the ray diagrams:
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
17. Ray Tracing and the Mirror Equation
17. Ray Tracing and the Mirror Equation
Here are the sign conventions for concave and convex mirrors:
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