Reflection from Plane Mirrors Explain the law of reflection. Distinguish between specular and diffuse reflection. Locate the images formed by plane mirrors. In this section you will: Section 17.1

Reflection from Plane Mirrors The Law of Reflection Section 17.1 When you look at the surface of a body of water you don’t always see a clear reflection. Sometimes, the wind causes ripples in the water, and passing boats create waves. Disturbances on the surface of the water prevent the light from reflecting in a manner such that a clear reflection is visible.

Reflection from Plane Mirrors Almost 4000 years ago, Egyptians understood that reflection requires smooth surfaces. They used polished metal mirrors to view their images. Sharp, well-defined, reflected images were not possible until 1857, however, when Jean Foucault, a French scientist, developed a method of coating glass with silver. Modern mirrors are produced using ever-increasing precision. They are made with greater reflecting ability by the evaporation of aluminum or silver onto highly polished glass. The Law of Reflection Section 17.1

Reflection from Plane Mirrors What happens to the light that is striking a book? When you hold the book up to the light, you will see that no light passes through it. An object like this is called opaque. Part of the light is absorbed, and part is reflected. The absorbed light spreads out as thermal energy. The behavior of the reflected light depends on the type of surface and the angle at which the light strikes the surface. The Law of Reflection Section 17.1

Reflection from Plane Mirrors When a wave traveling in two dimensions encounters a barrier, the angle of incidence is equal to the angle of reflection of the wave. This same two-dimensional reflection relationship applies to light waves. The Law of Reflection Section 17.1

Reflection from Plane Mirrors The Law of Reflection Section 17.1 Click image to view the movie.

Reflection from Plane Mirrors Consider the beam of light shown below. Smooth and Rough Surfaces Section 17.1 All of the rays in this beam of light reflect off the surface parallel to one another.

Reflection from Plane Mirrors This occurs only if the reflecting surface is not rough on the scale of the wavelength of light. Such a surface is considered to be smooth relative to the light. Specular reflection is caused by a smooth surface, in which parallel light rays are reflected in parallel. Smooth and Rough Surfaces Section 17.1

Reflection from Plane Mirrors What happens when light strikes a surface that appears to be smooth, but actually is rough on the scale of the wavelength of light, such as the page of a textbook or a white wall? Is light reflected? Smooth and Rough Surfaces Section 17.1

Reflection from Plane Mirrors The figure shows a beam of light reflecting off a sheet of paper, which has a rough surface. Smooth and Rough Surfaces Section 17.1 All of the light rays that make up the beam are parallel before striking the surface, but the reflected rays are not parallel.

Reflection from Plane Mirrors Diffuse reflection is caused by the scattering of light off a rough surface. Smooth and Rough Surfaces Section 17.1 The law of reflection applies to both smooth and rough surfaces. For a rough surface, the angle that each incident ray makes with the normal equals the angle that its reflected ray makes with the normal. However, on a microscopic scale, the normals to the surface locations where the rays strike are not parallel. Thus, the reflected rays cannot be parallel. In this case, a reflected beam cannot be seen because the reflected rays are scattered in different directions.

A plane mirror is a flat, smooth surface from which light is reflected by specular reflection. An object is a source of light rays that are to be reflected by a mirrored surface. Objects and Plane-Mirror Images Section 17.1 Reflection from Plane Mirrors An object can be a luminous source, such as a lightbulb, or an illuminated source, such as a girl, as shown in the figure. To understand reflection from a mirror, you must consider the object of the reflection and the type of image that is formed.

Reflection from Plane Mirrors Looking at yourself in a mirror, you can see that your image appears to be the same distance behind the mirror as you are in front of the mirror. You also see that your image is oriented as you are, and it matches your size. This is where the expression mirror image originates. If you move toward the mirror, your image moves toward the mirror. If you move away, your image also moves away. Properties of Plane-Mirror Images Section 17.1

A plane mirror produces an image with the same orientation as the object. However, there is a difference between you and the appearance of your image in a mirror. In the figure, the ray that diverges from the right hand of the boy converges at what appears to be the left hand of his image. Left and right appear to be reversed by a plane mirror. Image Orientation Section 17.1 Reflection from Plane Mirrors

Why, then, are top and bottom not also reversed? This does not happen because a plane mirror does not really reverse left and right. The mirror only reverses the boy’s image such that it is facing in the opposite direction as the boy, or, in other words, it produces a front-to-back reversal. Image Orientation Section 17.1 Reflection from Plane Mirrors

Refraction of Light When you shine a narrow beam of light at the surface of a piece of glass, it bends as it crosses the boundary from air to glass. The bending of light, called refraction, was first studied by René Descartes and Willebrord Snell around the time of Kepler and Galileo. Snell’s Law of Refraction Section 18.1

Refraction of Light The angle of incidence, θ 1, is the angle at which the light ray strikes the surface. It is measured from the normal to the surface. Snell’s Law of Refraction Section 18.1

Refraction of Light The angle of refraction, θ 2, is the angle at which the transmitted light leaves the surface. It also is measured with respect to the normal. Snell’s Law of Refraction Section 18.1

Refraction of Light Snell found that when light went from air into a transparent substance, the sines of the angles were related by the equation sin θ 1 /sin θ 2 = n. Here, n is a constant that depends on the substance, not on the angles, and is called the index of refraction. Snell’s Law of Refraction Section 18.1 The relationship found by Snell is also valid when light goes across a boundary between any two materials.

Refraction of Light Section 18.1 Snell’s Law of Refraction According to Snell’s Law of Refraction, the product of the index of refraction of the first medium and the sine of the angle of incidence is equal to the product of the index of refraction of the second medium and the sine of the angle of refraction. Snell’s Law of Refraction

Refraction of Light When light goes from air to glass, it moves from material with a lower index of refraction to one with higher index of refraction. That is, n 1 < n 2. So, the light beam is bent toward the normal to the surface. Snell’s Law of Refraction Section 18.1

Refraction of Light When light travels from glass to air it moves from material having a higher index of refraction to one with a lower index. In this case, n 1 > n 2. So, the light is bent away from the normal. Note that the direction of the ray when it leaves the glass is the same as it was before it struck the glass, but it is shifted from its original position. Snell’s Law of Refraction Section 18.1

Refraction of Light The index of refraction of a medium is equal to the speed of light in a vacuum divided by the speed of light in the medium. Index of Refraction Section 18.1 Index of Refraction This definition of the index of refraction can be used to find the wavelength of light in a medium.

Refraction of Light On a hot summer day, as you drive down a road, you see what appears to be the reflection of an oncoming car in a pool of water. The pool, however, disappears as you approach it. Mirages Section 18.1

Refraction of Light The mirage is the result of the Sun heating the road. The hot road heats the air above it and produces a thermal layering of air that causes light traveling toward the road to gradually bend upward. This makes the light appear to be coming from a reflection in a pool. Mirages Section 18.1

Refraction of Light The speed of light in a medium is determined by interactions between the light and the atoms that make up the medium. Temperature and pressure are related to the energy of particles on the atomic level. The speed of light, and therefore, the index of refraction for a gaseous medium, can change slightly with temperature. In addition, the speed of light and the index of refraction vary for different wavelengths of light in the same liquid or solid medium. Dispersion of Light Section 18.1

White light separates into a spectrum of colors when it passes through a glass prism. This phenomenon is called dispersion. Refraction of Light Dispersion of Light Section 18.1

If you look carefully at the light that passes through a prism, you will notice that violet is refracted more than red. This occurs because the speed of violet light through glass is less than the speed of red light through glass. Refraction of Light Dispersion of Light Section 18.1

Refraction of Light Violet light has a higher frequency than red light, which causes it to interact differently with the atoms of the glass. This results in glass having a slightly higher index of refraction for violet light than it has for red light. Dispersion of Light Section 18.1

Refraction of Light A prism is not the only means of dispersing light. A rainbow is a spectrum formed when sunlight is dispersed by water droplets in the atmosphere. Rainbows Section 18.1

Refraction of Light Sunlight that falls on a water droplet is refracted. Because of dispersion, each color is refracted at a slightly different angle. Rainbows Section 18.1

Refraction of Light At the back surface of the droplet, some of the light undergoes internal reflection. On the way out of the droplet, the light once again is refracted and dispersed. Rainbows Section 18.1

Refraction of Light Although each droplet produces a complete spectrum, an observer positioned between the Sun and the rain will see only a certain wavelength of light from each droplet. The wavelength depends on the relative positions of the Sun, the droplet, and the observer. Rainbows Section 18.1

Refraction of Light Because there are many droplets in the sky, a complete spectrum is visible. The droplets reflecting red light make an angle of 42° in relation to the direction of the Sun’s rays; the droplets reflecting blue light make an angle of 40°. Rainbows Section 18.1