Physics 102-002 Announcements

Physics 102-002Announcements • WebAssign – • No Chapter 26 Homework • Chapter 28 due next Wednesday • Exam 3 Corrections due This Wed, Apr 25 • Final Exam May 7, 5:30-7:30, in regular classroom Picture: Image of diffraction of the beam of a Helium-Neon laser when passed through a single slit.

Class Schedule

Chapter 28Reflection and Refraction • Reflection and Principle of Least Time • Law of Reflection • Plane Mirrors • Diffuse Reflection • Refraction • Cause of Refraction • Dispersion • Rainbows • Total Internal Reflection • Lenses (and Image Formation by Lenses) • Lens Defects Next time

Reflection Reflection is the change in direction of a wave front at an interface between two dissimilar media so that the wave front returns into the medium from which it originated. (Common examples include the reflection of light, sound and water waves, but we’re focused on light waves, of course). A mirror provides the most common model for specular light reflection and consists of a glass sheet in front of a metallic coating where the reflection actually occurs. Reflection is enhanced in metals by suppression of wave propagation beyond the surface. It is also possible (even likely) for reflection to occur from the surface of transparent media, such as water or glass. In fact, reflection of light may occur whenever light travels from one medium into another if the speed of light is different in the two media. In most cases, a certain fraction of the light is reflected from the interface, and the rest is refracted (transmitted through the second medium). Reflection happens because electrons in the atoms making up something get “energized” by the light that hits them, and the electrons re-emit the incident light at the same frequency. When a page in your text book is illuminated by white light, it looks white … its electrons re-emit all the frequencies that hit them. The ink absorbs most of the light (of all frequencies) that hits it, and so it looks black. Fermat’s Principle of Least Time: Out of all the paths that light might travel in going from one point to another, it always travels the path that takes the least time (not always the shortest distance). A Black triggerfish reflecting in the water surface.

Law of Reflection Light is known to behave in a very predictable manner. If a ray of light could be observed approaching and reflecting off of a flat mirror, then the behavior of the light as it reflects would follow a predictable law known as the law of reflection. The diagram to the right illustrates the law of reflection. In the diagram, the ray of light approaching the mirror is known as the incident ray. The ray of light which leaves the mirror is known as the reflected ray. At the point of incidence where the incident ray strikes the mirror, a line can be drawn perpendicular to the surface of the mirror; this line is known as the normal line. The angle between the incident ray and the normal is known as the angle of incidence. The angle between the reflected ray and the normal is known as the angle of reflection. The Law of Reflection states that when a ray of light reflects off a surface, the angle of incidence is equal to the angle of reflection. This is another way of saying that the light follows the path that takes the least time. If you’ve ever played pool, you know that a pool ball bounces off a cushion at the same angle at which it hit the cushion … same principle applies here! Physics Place figure

Question 1

Question 1 Answer

Plane Mirrors In order to see the image of an object in a mirror, you must sight at the image; when you sight at the image, light will come to your eye along that line of sight. The image location is thus located at that position where observers are sighting when viewing the image of an object. It is the location behind the mirror where all the light appears to come from. In the diagram below, three individuals are sighting at the image of an object along three different lines of sight. Each person sees the image due to the reflection of light off the mirror in accordance with the law of reflection. When each line of sight is extended backwards, each line will intersect at the same point. This point is the image point of the object. The image appears to be the same distance behind the mirror as the real object is in front of it, and it appears to be the same size. The image is a virtual image, because the light really doesn’t come from that point. If the mirror were curved … either outward (convex), or inward (concave), the sizes and distances of the object and image are no longer equal.

Diffuse Reflection Reflection off of rough surfaces such as clothing, paper, and the asphalt roadway leads to a type of reflection known as diffuse reflection. Whether the surface is microscopically rough or smooth has a tremendous impact upon the subsequent reflection of a beam of light. The diagram below depicts two beams of light incident upon a rough and a smooth surface. A light beam can be thought of as a bundle of individual light rays which are traveling parallel to each other. Each individual light ray of the bundle follows the law of reflection. If the bundle of light rays is incident upon a smooth surface, then the light rays reflect and remain concentrated in a bundle upon leaving the surface. On the other hand, if the surface is microscopically rough, the light rays will reflect and diffuse in many different directions. A surface can cause diffuse reflection at one wavelength, and specular (like a mirror) reflection at another wavelength. The key is the amount of surface roughness compared to the wavelength of the light. If the roughness on the surface is less than about one eighth the wavelength, there will be very little diffuse reflection. Physics Place figure

Question 2

Question 2 Answer h/2

Refraction Refraction is the change in a light wave’s direction that occurs as the light passes across the boundary between two media. The transmission of light across a boundary between two media is accompanied by a change in both the speed and wavelength of the wave. The light wave not only changes directions at the boundary, it also speeds up or slows down and transforms into a wave with a larger or a shorter wavelength. The only time that a wave can be transmitted across a boundary, change its speed, and still not refract is when the light wave approaches the boundary in a direction which is perpendicular to it. As long as the light wave changes speed and approaches the boundary at an angle, refraction is observed. Light Traveling from a Fast to a Slow Medium If a ray of light passes across the boundary from a material in which it travels fast into a material in which travels slower, then the light ray will bend towards the normal line. Light Traveling from a Slow to a Fast Medium … will bend away from the normal line. Now lets look at another analogy to help us understand refraction. Suppose a tractor is moving across an asphalt surface towards a plot of grass (as shown in the diagram). Upon entering the grass, the tractors' wheels will sink into the surface and slow down. Upon exiting the plot of grass on the opposite side, the tractor wheels will speed up and achieve their original speed.

Air Air Glass A B a c C Refraction (cont’d) Least Time Principle … remember! Of all the possible paths that light might take to get from one point to another, it always takes the path that requires the least amount of time. The swimmer analogy given in the book also helps to understand that it’s the change in the speed of light that causes refraction. In a prism, the angled sides cause the colors that comprise white light to emerge separately on the other side. When light goes through glass, if it hits the glass on the “normal”, it won’t refract. If the light hits at an angle to the normal, it will take the path of least time to go from point A to point C.

Question 3 Arthur Podd's method of fishing involves spearing the fish while standing on the shore. The actual location of a fish is shown in the diagram below. Because of the refraction of light, the observed location of the fish is different than its actual location. Indicate on the diagram the approximate location where Arthur observes the fish to be. Must Arthur aim above or below where the fish appears to be in order to strike the fish? • Above • Below

Question 3 Answer Arthur Podd's method of fishing involves spearing the fish while standing on the shore. The actual location of a fish is shown in the diagram below. Because of the refraction of light, the observed location of the fish is different than its actual location. Indicate on the diagram the approximate location where Arthur observes the fish to be. Must Arthur aim above or below where the fish appears to be in order to strike the fish? • Above • Below Since light from the fish refracts away from the normal when it goes from water to air, the image of the fish will appear to be higher than the fish really is.

Physics 102-002 Announcements