# 4.1 The Concepts of Force and Mass

Chapter 25 The Reflection of Light: Mirrors Copyright 2015 John Wiley & Sons, Inc. All rights reserved. Wave Fronts and Rays A hemispherical view of a sound wave emitted by a pulsating sphere.

The rays are perpendicular to the wave fronts. Copyright 2015 John Wiley & Sons, Inc. All rights reserved. Wave Fronts and Rays At large distances from the source, the wave fronts become less and less curved. Copyright 2015 John Wiley & Sons, Inc. All rights reserved.

Wave Fronts and Rays A ray refers to a narrow stream of light energy. Scientifically, a ray is the direction of the path taken by light. A beam is a stream of light energy. A beam may be represented by a number of rays which may be either diverging, converging or parallel. Light travels in a straight line (Rectilinear Propagation of Light) Student Research a. Read on how shadows are formed and be prepared to discuss in

class. b. Read on how eclipses are formed and be prepared to discuss in class. c. Read on the nature of light and be prepared to discuss in class. Copyright 2015 John Wiley & Sons, Inc. All rights reserved. The Reflection of Light LAWS OF REFLECTION 1. The incident ray, the reflected ray, and the normal

to the surface all lie in the same plane. 2. The angle of incidence equals the angle of reflection. Copyright 2015 John Wiley & Sons, Inc. All rights reserved. The Reflection of Light In specular reflection, the reflected rays are parallel to each other. Specular Reflection: Rays striking a smooth and highly polished surface. Examples: Highly Polished smooth glass and mirrors.

Diffuse Reflection: Rays striking an irregular surface. Copyright 2015 John Wiley & Sons, Inc. All rights reserved. The Formation of Images by a Plane Mirror The persons right hand becomes the images left hand. The image has five properties: 1. It is upright. 2. It is the same size as you are. 3. The image is as far behind the

mirror are you are in front of it. 4. Laterally Inverted. (Right Hand of Object becomes Left Hand of Image) 5. Image is Virtual (Not Real). Image is said to be virtual if it cannot be produced on a screen. Another way of describing virtual image is that it is produced at a place where the reflected rays appear to intersect. Copyright 2015 John Wiley & Sons, Inc. All rights reserved.

The Formation of Images by a Plane Mirror A ray of light from the top of the chess piece reflects from the mirror. To the eye, the ray seems to come from behind the mirror. Because none of the rays actually emanate from the image, it is called a virtual image. Copyright 2015 John Wiley & Sons, Inc. All rights reserved. The Formation of Images by a Plane Mirror

The geometry used to show that the image distance is equal to the object distance. Copyright 2015 John Wiley & Sons, Inc. All rights reserved. The Formation of Images by a Plane Mirror Conceptual Example. Multiple Reflections A person is sitting in front of two mirrors that intersect at a right angle. The person sees three images of herself. Why are there three, rather than two, images?

Student Research: How many images is an observer expected to see if an object is placed in between two parallel plane mirrors? Draw a ray diagram to validate your response. Example of a ray diagram is shown above. Copyright 2015 John Wiley & Sons, Inc. All rights reserved. Spherical Mirrors If the inside surface of the spherical mirror is polished, it is a concave mirror. If the outside surface is polished, is it a convex mirror. The law of reflection applies, just as it does for a plane mirror. The principal axis of the mirror is a straight line drawn through the

center of curvature and the midpoint of the mirror. Copyright 2015 John Wiley & Sons, Inc. All rights reserved. Spherical Mirrors (Concave Mirrors) A point on the tree lies on the principal axis of the concave mirror. Rays from that point that are near the principal axis cross the axis at the image point. Copyright 2015 John Wiley & Sons, Inc. All rights reserved.

Spherical Mirrors (Concave Mirrors) Light rays near and parallel to the principal axis are reflected from the concave mirror and converge at the focal point. The focal point also known as the principal focus of a spherical mirror is that point on the principal axis to which all rays originally parallel and close to the principal axis converge or from which they diverge , after reflection from the mirror. The focal length is the distance between the focal point and the mirror. Copyright 2015 John Wiley & Sons, Inc. All rights reserved.

Spherical Mirrors (Concave Mirrors) The focal point of a concave mirror is halfway between the center of curvature of the mirror C and the mirror at B. f 12 R Copyright 2015 John Wiley & Sons, Inc. All rights reserved. Spherical Mirrors (Concave Mirrors) Rays that lie close to the principal axis are called paraxial rays.

Rays that are far from the principal axis do not converge to a single point. The fact that a spherical mirror does not bring all parallel rays to a single point is known as spherical aberration. Copyright 2015 John Wiley & Sons, Inc. All rights reserved. Spherical Mirrors (Concave) Copyright 2015 John Wiley & Sons, Inc. All rights reserved. Spherical Mirrors (Concave)

Additional diagrams of Images Formed by Concave Mirrors These images will be produced on the board in class. Note: A real Image is formed by the actual intersection of rays, wheras a virtual image is one formed by the apparent intersection of rays when their directions have been produced backwards. Copyright 2015 John Wiley & Sons, Inc. All rights reserved. Spherical Mirrors (Convex)

When paraxial light rays that are parallel to the principal axis strike a convex mirror, the rays appear to originate from the focal point. f 12 R Copyright 2015 John Wiley & Sons, Inc. All rights reserved. The Formation of Images by Spherical Mirrors CONCAVE MIRRORS

This ray is initially parallel to the principal axis and passes through the focal point. This ray initially passes through the focal point, then emerges parallel to the principal axis. This ray travels along a line that passes through the center. Copyright 2015 John Wiley & Sons, Inc. All rights reserved.

The Formation of Images by Spherical Mirrors Image formation and the principle of reversibility Copyright 2015 John Wiley & Sons, Inc. All rights reserved. The Formation of Images by Spherical Mirrors When an object is located between the focal point and a concave mirror, and enlarged, upright, and virtual image is produced.

Ray 1 is initially parallel to the principal axis and appears to originate from the focal point. Ray 2 heads towards the focal point, emerging parallel to the principal axis. Ray 3 travels toward the center of curvature and reflects back on itself. Copyright 2015 John Wiley & Sons, Inc. All rights reserved. The Formation of Images by Spherical Mirrors The virtual image is diminished in size and upright. Copyright 2015 John Wiley & Sons, Inc. All rights reserved.

The Mirror Equation and Magnification f focal length d o object distance d i image distance m magnification Copyright 2015 John Wiley & Sons, Inc. All rights reserved. The Mirror Equation and Magnification

These diagrams are used to derive the mirror equation. 1 1 1 do di f hi di m ho

do Copyright 2015 John Wiley & Sons, Inc. All rights reserved. The Mirror Equation and Magnification Example 5 A Virtual Image Formed by a Convex Mirror A convex mirror is used to reflect light from an object placed 66 cm in front of the mirror. The focal length of the mirror is -46 cm. Find the location of the image and the magnification.

1 1 1 1 1 0.037 cm 1 d i f d i 46 cm 66 cm d i 27 cm

di 27 cm m 0.41 do 66 cm Copyright 2015 John Wiley & Sons, Inc. All rights reserved. The Mirror Equation and Magnification

Summary of Sign Conventions for Spherical Mirrors f is for a concave mirror. f is for a convex mirror. d o is if the object is in front of the mirror. d o is if the object is behind the mirror. d i is if the object is in front of the mirror (real image). d i is if the object is behind the mirror (virtual image). m is for an upright object. m is for an inverted object.