Ch 9, Mirrors, Lenses and Optical Systems

9.1 Geometrical Optics & Plane Mirrors  In this chapter the dimensions of the mirrors, prisms and lenses discussed are much greater than the wavelength of light and hence diffraction effects can be ignored. In these circumstances light travels in straight lines according to the laws of reflection and refraction, and so pathways are accurately represented with rays. These conditions are called the conditions of geometrical optics.

Ray Tracing  To investigate the images produced by mirrors and lenses ray tracing can be carried out. Using rays, known pathways of light are modelled on a scaled, two-dimensional diagram and the characteristics of the resulting image can be identified. The image can then be fully described by its:  nature—Is the image real or virtual? (discussed later)  orientation—Is the image upright or inverted?  position—Where is the image in relation to the mirror?  size (including magnification)—What is the height of the image? By what factor has the size of the image changed?

Images in a Plane Mirror The object and image are exactly the same size. All images formed by plane mirrors have the following characteristics:  The image is always upright.  The image is the same distance behind the mirror as the object is in front.  The image is the same size as the object.

Images in a Plane Mirror  Use ray tracing to locate the image of the pom-pom on the top of this girl's hat, which is 50 cm from the mirror as shown.

9.1 Questions  4, 7, 8, 9

9.2 Applications of Curved Mirrors: Concave Mirrors  All curved mirrors are either concave or convex. A concave mirror is curved like the inside of the bowl of a spoon, whereas a convex mirror is shaped like the back of a spoon. (One way to remember which is which is to recall that a concave mirror forms a small cave or may cave in.)

Watch

Concave Mirrors

Ray Diagrams Particular conventions apply to the construction of a ray diagram (Figure 9.12).  A vertical line called the optical axis represents the reflecting surface, i.e. the back of the mirror. Although the mirror surface is curved, the optical axis is a straight vertical line. A ray diagram tends to use a much larger vertical scale than horizontal scale, thus allowing the mirror to be represented by a straight line with little loss of accuracy.  The optical axis is perpendicular to the principal axis, and the pole, P, is placed at the intersection between the optical axis and the principal axis. A small curved mirror symbol is placed here to indicate the type of mirror being used.  The principal focus of the mirror, F, and its centre of curvature, C, are located on the principal axis to scale.  Traditionally, the object is on the left of the optical axis, along with the eye that will view the image. The object is usually represented as a small vertical arrow.

Ray Diagrams: Concave Mirror

Concave Mirror Ray Tracing

Ray Diagram Examples

Summary of Images formed by Concave Mirrors

Magnification

Example  A man stands in front of his shaving mirror and is disappointed with the image he sees. The focal length of the concave mirror is 50 cm, and he is standing 1.5 m from its pole. Use a ray diagram to explain what he sees in the mirror.

9.2 Questions  3, 4, 5, 6, 9

9.3 Convex Mirrors

Convex Mirror Ray Tracing

Images formed by Convex Mirror  All images are upright, virtual and diminished. As the object is brought closer to the mirror, the image increases in size, but it will never be the same size as the object.

Example  A shop uses a convex mirror of focal length 2.0 m for security purposes. If a person 1.5 m tall is standing 4.0 m from the mirror, describe the nature of the image seen. What is the magnification of the image?

Mirror Formula  The mirror formula provides the relationship between the focal length of a mirror, f, the distance of the object from the pole of the mirror, u, and the distance of the image from the pole of the mirror, v. The relationship is:

Mirror Formula Example  A person stands 30 cm from the pole of a concave mirror and an inverted image is formed 60 cm from the mirror. What is the focal length of the mirror?

9.3 Questions  2, 9