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Chapter Review

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As discussed in the previous chapter, light is an electromagnetic wave. However, understanding the behavior of light does not always require a wave analysis. In this chapter and the next, we study the branch of physics, called geometrical optics, in which conditions are such that the wave nature of light can be "glossed over" while still accurately describing its behavior.

26-1   The Reflection of Light

In the study of geometrical optics we think of light as rays traveling along a straight-line path. In terms of the propagating electromagnetic wave, we can track the crests of these waves (or any specific phase point). The collection of crests at a given phase can be imagined to form surfaces called wave fronts. Within this approximation, the light rays are perpendicular to the wave fronts and point in the direction of their propagation. As a light wave gets further away from the source the wave fronts are so spread out that the surfaces are approximately planar; these waves are called plane waves and they give rise to parallel rays.

The reflection of light from a smooth boundary obeys a simple law called the law of reflection. This law says that the angle that the incident ray makes with the normal to the reflecting surface, called the angle of incidence q_i, is equal to the angle that the reflected ray makes with the normal to the surface, called the angle of reflection q_r. Also, the incident ray, the normal line, and the reflected ray all lie in the same plane.

Practice Quiz

An incident light ray makes an angle of 33o with the normal to the surface of a plane mirror. What angle does the reflected ray make with the surface of the mirror? 0o 33o 66o 57o [None of the above.]

26-2   Forming Images with a Plane Mirror

A plane mirror is one that is perfectly flat. When you look at your reflection in a plane mirror what you see is called an image of yourself. The source that is being reflected in the mirror (you) is called the object. Using the law of reflection, several results about reflection with a plane mirror can be found:

• The distance between the object and the mirror, called the object distance d_o, is equal to the distance between the image, on the opposite (back) side of the mirror, and the mirror, called the image distance d_i.
  


• The image is right-side-up, referred to as upright.
  


• The images is the same size as the object.

Left and right appear to be reversed in a mirror. This occurs because the image is facing you. Just as when a person faces you, their right hand is on your left, and vice versa.

Practice Quiz

An object is 5.0 m in front of a plane mirror. How far away from the mirror is its image? 0.0 m 2.5 m 5.0 m 10.0 m 15.0 m

Physlet Illustration: Reflection in a Plane Mirror
In this simulation, a 1-cm high object is placed in front of a plane mirror. How and where is the image formed? What are the characteristics of the image?
Hints: Drag the object back and forth in front of the mirror, and study the image produced. If you click your mouse at any point along a light ray, and then drag the mouse cursor to the right along the ray, you can measure the angle of that ray with respect to a line normal to the mirror. Do so, and verify that the law of reflection governs the behavior of each light ray that strikes the mirror's surface. Do the rays that leave the top of the object, traveling in different directions and reflecting off the mirror, ever come together again? Do those rays, having reflected from the mirror, appear to emanate from the same point behind the mirror? Is this, then, a real or a virtual image? The mirror is located at x = 2.0 cm. Where are the object and image located, relative to the mirror? How does the image height compare to the object's height? Is the image upright or inverted?

26-3   Spherical Mirrors

A spherical mirror has the shape of a section of a sphere. If the reflecting surface is on the outside of this spherical section it is called a convex mirror; if the reflecting surface is on the inside it is called a concave mirror. The principal axis of the mirror is the line that passes through the center of the mirror (often called the vertex) perpendicular to the surface. A distance R away from the vertex along the principal axis is a point called the center of curvature C, where R is the radius of the sphere from which the spherical section of mirror was taken (often called the radius of curvature). The point C would be located at the center of the sphere.

If light rays that are parallel to the principal axis, and lie close to it (paraxial rays), are incident on a sperical mirror, they will either converge to (for a concave mirror) or diverge from (for a convex mirror) points a distance of magnitude f from the vertex, called the focal length. The point on the principal axis a distance of one focal length away from the vertex is called the focal point. For a spherical mirror the focal length is given by

,

where the + sign applies to concave mirrors and the - sign applies to convex mirrors. The full reasoning behind these differences in sign will be discussed below. Basically, the positive sign means that the focal point is in front of the mirror and the negative sign means that it is behind the mirror.

Practice Quiz

The center of a curvature of a convex, spherical mirror is located 50 cm away from its vertex. What is its focal length? 25 cm -25 cm 50 cm -50 cm [None of the above.]

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