Optics 1 Ray Optics or Geometrical Optics In many circumstances we can ignore the wave nature of light and assume that light is a stream of particles that travel in straight lines called rays For instance if a light wave from a point source passes through an aperture a hole that is very large compared to the wavelength of light then a beam or ray of light is produced We ll see later why you need the hole diameter large compared to the wavelength aperture diameter D speed c source beam or ray of light if D Mirrors When light reflects from a dull surface the rays scatter in all directions so observers eye light ray can see reflected rays from all directions eye dull surface Why does light scatter from the surface of a material The incident light ray is an electromagnetic wave The oscillating electric field of the EM waves shakes the charges electrons and protons in the surface of the material The shaking charges create new electromagnetic waves which radiate outward in all directions When a ray of light scatters from the surface of a smooth mirror the ray is reflected in one direction only The incident angle is equal to the reflected angle i r i r mirror Why does the light reflected from a smooth surface scatter in one direction only When you study Last update 11 16 2009 Dubson Phys1120 Notes University of Colorado Optics 2 interference and diffraction you will see that when the surface is smooth the scattered rays interfere destructively cancel in all directions except the one direction for which i f dull shiny Any surface is shiny and mirror like if it is smooth compared to the wavelength of light visible 500 nm A surface that is dull in visible light can be shiny in the infrared Rays from a point source reflected from a mirror appear to be coming from a point behind the mirror A virtual image occurs when rays mirror appear to be coming from a point in space but eye are not really Here s the trick to analyzing mirror problems redraw the incident virtual image reflected rays as straight lines source d d Refraction and Snell s Law Any transparent medium air water glass etc can be characterized by a dimensionless number called the index of refraction n c v speed of light in vacuum speed of light in the medium material index n The speed of light in a vacuum c is an absolute maximum speed the speed of light in a medium is always less than c So in a medium v c always n c v 1 always Last update 11 16 2009 vacuum 1 air 1 0003 1 water 1 33 Lucite 1 51 glass 1 45 1 75 diamond 2 42 Dubson Phys1120 Notes University of Colorado Optics 3 When a ray of light passes from 1 medium to another the ray is bent or refracted according to Snell s Law n1 sin 1 n 2 sin 2 medium 1 In optics angles are always measured with respect to the normal perpendicular direction Notice that the ray is closer to the normal in the medium 2 2 normal 1 medium with the larger index n The larger the change in n the more the ray is bent interface Why does light slow down and change direction when passing from vacuum into a medium The oscillating E field of the incident EM waves shakes the charges in the medium The shaking charges create a new EM wave which interferes with the original wave to make a new net wave that moves more slowly and in a different direction In general when a ray is incident on an interface there are both reflected and refracted rays n1 reflected incident n2 n1 refracted If the ray passes from a higher n to a lower n material the ray is bent away from the normal If the incident angle is large enough you get total internal reflection and no refracted ray no refracted ray n1 n2 n2 c Last update 11 16 2009 c c Dubson Phys1120 Notes University of Colorado Optics 4 Example of total internal reflection What is the critical angle c for a light ray in water at an air water interface Medium 1 water medium 2 air Index of water n1 nw 1 33 Index of air n2 na 1 We start with Snell s Law n1 sin 1 n 2 sin 2 n w sin c 1 sin 90o 1 1 sin c 1 nw 1 1 c sin 1 sin 1 1 33 n w 48 8o Light pipes guide light rays by total internal reflection Last update 11 16 2009 Dubson Phys1120 Notes University of Colorado Optics 5 Lenses and image formation Images can be formed with lenses or mirrors Most texts starts with a discussion of mirrors we ll start with lenses Key ideas in lens design 1 For a ray passing through a flat plate of glass with parallel air glass air surfaces the incoming ray and the outgoing ray are parallel The refraction ray bending at the air glass interface on the way in is exactly undone by the refraction at the glass air interface on the way out 2 For a wedge shaped piece of glass like a prism the ray is bent toward the thicker end From these two ideas we see that a convex lens one that is thick in the middle and thin on the edges tends to focus a bundle of parallel rays to a point focal point parallel rays focal length f 0 The center ray is not bent because the surfaces are parallel The edge rays are bent toward the thicker part A convex lens is also called a converging lens since the rays converge on the focus The focal length f is the distance from the lens to the focal point where all the parallel rays from the other side of the lens come to a focus The focal length depends on both the index of refraction n of the glass and the shape of the lens short f Last update 11 16 2009 long f Dubson Phys1120 Notes University of Colorado Optics 6 Parallel rays are produced by distant point sources light rays from a star in the sky are parallel far from source small bundle of rays is nearly parallel point source Diverging lens or concave lens Thin in the middle thick at the parallel rays edges Remember rays bend toward the thicker end focus focal length f 0 You can form images on a screen of distant objects using a converging lens 1 2 two distant point sources from source 1 from source 2 Last update 11 16 2009 lens screen f focal plane Dubson Phys1120 Notes University of Colorado Optics 7 If the screen is placed at the focal plane of the lens one focal length f away from the lens then you will see two points of light on the screen which are the images of point sources 1 and 2 These are real images A real image as opposed to …
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