The Ray model of Light Over distances of a terrestrial scale light travels in a straight line. The path of a laser is now the best way we have of defining a straight line. The model of light which assumes that light travels in straight lines is called the ray model of light. We know that light is really a E-M wave, but the ray model of light minimizes this property and yet produces useful ways of calculating effects with light. Reflection Fig 23.2 In describing the effects of light and a surface we are always going to define angles with respect to the normal to the surface. The rule for the reflection of light at a surface is that the incident angle is equal to the reflected angle. The reflection of light off a smooth surface is called specular reflection and it preserves the image of objects seen in reflection, rather than aspects of the reflecting surface If the reflecting surface is rough the image of the object seen in reflection is not preserved. Figrue 23.4 1.
The way the eye forms an image of an object in reflection is the same as the way the eye forms the image of any object All the rays from a single point on the object are brought together at a point on the retina of the eye. The reflected object looks as though it were actually behind the mirror. Figure 23-6 The image of the object behind the mirror is called a virtual image. The defining characteristic of a virtual image is that there is no actual light there. A photographic film would not record anything ar a virtual image. The opposite of a virtual image is a real image, in which there is actual light and a so a photographic film can record a real image. From the figure and some geometry you can see that the distance of the virtual image behind the mirror is the same as the distance of the real object from the front of the mirror. It is useful to have a mirror which can reflect our whole image so we can see if we are sartorially fit to go out into the world in the morning. Unless you stand very close to a mirror, a mirror capable of reflecting you full image need not be actually the same height as you are as seen here. Fig 23-7 2.
Spherical Mirrors The mirrors we have discussed so far have all been plane mirrors, with which the size of the reflected image is the same as the size of the reflected object. For some applications it is useful for the size of the reflected image be different. Convex mirrors are used to give a wider field of view than a plane mirror, that is they make the reflected images smaller than the actual objects. This makes the object seem farther away as is stated in the warning on the cars convex rear view mirror. A concave mirror makes images larger, and is useful for looking at small things. 3.
Fig 23-9 23-8 Focal point and Focal Length If we use a spherical mirror to look at an object which is very far away, say the sun or the moon, the rays which hit the mirror will be almost exactly parallel to each other. Parallel rays are all reflected so that they intersect very close to a single point. If the mirror were parabolic, rather than spherical, the reflected ray would actually intersect at a single point. The point which is the approximate intersection of parallel rays is defined as the focal point. The distance of the focal point from the mirror is called the focal length of the mirror. Figure 23-12 This drawing shows that the focal length is ½ of the radius of the spherical mirror. The fact that spherical mirrors do not actually reflect parallel rays exactly at a point is called the spherical aberration, which you will measure in you lab. 4.
Image Formation by Ray Diagrams Fig 23-13 Ray 1 is drawn parallel to the axis and therefore on reflection it must pass through F Ray 2 goes from the object through F and therefore it must reflect parallel to the axis Ray 3 passes through the center of curvature, C, and therefore it is perpendicular to the mirror surface at the point of reflection and so passes back along its incident path. Fig 23-13 5.
Index of Refraction The speed of light in vacuum is called c and is 3.00 E8 m/s In all actual materials the speed of light is slower than it is in a vacuum. The ratio of the speed of light in vacuum to the speed of light in some material is the definition of the index of refraction n n= c v Refraction --- Snell's Law When a ray of light passes from one medium into another its direction changes. This change of direction is called refraction Fig 23-19 When passing from a less dense material to a more dense the ray bends toward the normal The angles that the ray makes with the normal in the second material is called the refraction angle. The angles and the refraction indexes are related by Snell'l Law n 1 sin 1=n 2 sin 2 6.
Refraction through a planar glass Example 23-6 Example 23-7 Total Internal Reflection --- Fiber Optics If a ray is going from a more dense material to a less dense material it will bend away from the normal. If it bends far enough away from the normal is will not emerge from the denser medium If we look at Snell's law for the case in which the ray goes along the interface, were get n 1 sin c =n 2 sin 90 c = Fig 23-34 7. n2 n1
example 23.7 Example 23-8 fig 23-25 8.
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Fiber Optics Fig 23-27 10.