Concept Summary

If you need more help with a concept, use the text examples and media noted next to the discussion or equation. Go to for:
Interactive LearningWare (ILW)—examples solved in a five-step interactive format.
Concept Simulations (CS)—animated text figures or animations of important concepts.
Interactive Solutions (IS)—models for certain types of problems in the chapter homework. The calculations are carried out interactively.
Self-Assessment Tests—qualitative and quantitative questions with extensive feedback.

Topic | Discussion | Learning Aids
Wave fronts Plane waves | 25.1 WAVE FRONTS AND RAYS Wave fronts are surfaces on which all points of a wave are in the same phase of motion. Waves whose wave fronts are flat surfaces are known as plane waves. |
Rays | Rays are lines that are perpendicular to the wave fronts and point in the direction of the velocity of the wave. |
Law of reflection | 25.2 THE REFLECTION OF LIGHT When light reflects from a smooth surface, the reflected light obeys the law of reflection:

a. | The incident ray, the reflected ray, and the normal to the surface all lie in the same plane.
b. | The angle of reflection equals the angle of incidence ; .

Virtual image | 25.3 THE FORMATION OF IMAGES BY A PLANE MIRROR A virtual image is one from which all the rays of light do not actually come, but only appear to do so. |
Real image | A real image is one from which all the rays of light actually do emanate. |
Plane mirror | A plane mirror forms an upright, virtual image that is located as far behind the mirror as the object is in front of it. In addition, the heights of the image and the object are equal. |

Use Self-Assessment Test 25.1 to evaluate your understanding of Sections 25.1, 25.2 and 25.3 .

Concave and convex mirrors | 25.4 SPHERICAL MIRRORS A spherical mirror has the shape of a section from the surface of a sphere. If the inside surface of the mirror is polished, it is a concave mirror. If the outside surface is polished, it is a convex mirror. |
Principal axis Paraxial rays | The principal axis of a mirror is a straight line drawn through the center of curvature and the middle of the mirror’s surface. Rays that are close to the principal axis are known as paraxial rays. Paraxial rays are not necessarily parallel to the principal axis. |
Radius of curvature | The radius of curvature R of a mirror is the distance from the center of curvature to the mirror. |
Focal point of a concave mirror | The focal point of a concave spherical mirror is a point on the principal axis, in front of the mirror. Incident paraxial rays that are parallel to the principal axis converge to the focal point after being reflected from the concave mirror. |
Focal point of a convex mirror | The focal point of a convex spherical mirror is a point on the principal axis, behind the mirror. For a convex mirror, incident paraxial rays that are parallel to the principal axis diverge after reflecting from the mirror. These rays seem to originate from the focal point. |
Spherical aberration | The fact that a spherical mirror does not bring all rays parallel to the principal axis to a single image point after reflection is known as spherical aberration. |
Focal length | The focal length f of a mirror is the distance along the principal axis between the focal point and the mirror. The focal length and the radius of curvature R are related by |
Concave mirror |

| (25.1)

Convex mirror |

| (25.2)

Ray tracing | 25.5 THE FORMATION OF IMAGES BY SPHERICAL MIRRORS The image produced by a mirror can be located by a graphical method known as ray tracing. |
| For a concave mirror, the following paraxial rays are especially useful for ray tracing (see Figure 25-18): |
Three rays for a concave mirror | Ray 1. This ray leaves the object traveling parallel to the principal axis. The ray reflects from the mirror and passes through the focal point. |
| Ray 2. This ray leaves the object and passes through the focal point. The ray reflects from the mirror and travels parallel to the principal axis. |
| Ray 3. This ray leaves the object and travels along a line that passes through the center of curvature. The ray strikes the mirror perpendicularly and reflects back on itself. |
| For a convex mirror, these paraxial rays are useful for ray tracing (see Figure 25-22a): |
Three rays for a convex mirror | Ray 1. This ray leaves the object traveling parallel to the principal axis. After reflection from the mirror, the ray appears to originate from the focal point of the mirror. |
| Ray 2. This ray leaves the object and heads toward the focal point. After reflection, the ray travels parallel to the principal axis. |
| Ray 3. This ray leaves the object and travels toward the center of curvature. The ray strikes the mirror perpendicularly and reflects back on itself. |
| 25.6 THE MIRROR EQUATION AND THE MAGNIFICATION EQUATION The mirror equation specifies the relation between the object distance do, the image distance di, and the focal length f of the mirror: |
Mirror equation |

| (25.3)

| The mirror equation can be used with either concave or convex mirrors. |
| The magnification m of a mirror is the ratio of the image height hi to the object height ho: |
Magnification |

| The magnification is also related to di and do by the magnification equation: |
Magnification equation |

| (25.4)

| The algebraic sign conventions for the variables appearing in these equations are summarized in the Reasoning Strategy at the end of Section 25.6. |

Use Self-Assessment Test 25.2 to evaluate your understanding of Sections 25.4, 25.5 and 25.6 .

Copyright © 2007 John Wiley & Sons, Inc. All rights reserved.