Optics-1Ray 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). Mirrors When light reflects from a dull surface, the rays scatter in all directions, so observers can see reflected rays from all directions. Whydoes light scatter from the surface of amaterial? The incident light ray is anelectromagnetic wave. The oscillatingelectric 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 angleLast update: 1/13/2019 Dubson Phys1120 Notes, University of Colorado speed csourcebeam or ray of light if D >> aperture diameter Ddull surfaceeyeeyelight rayOptics-2 i = rWhy does the light reflected from a smooth surfacescatter in one direction only? When you study 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 . Any surface is shiny and mirror-like if it issmooth compared to the wavelength of light visible 500 nm. A surface that is dull invisible light can be shiny in the infrared.Rays from a point source, reflected from amirror, appear to be coming from a point behind the mirror. A "virtual image" occurs when rays appear to be coming from a point in space, but are not really. Here's the trick to analyzing mirror problems: redraw the incident & reflected rays as straight lines.Refraction and Snell's LawAny transparent medium (air, water, glass, etc) can be characterized by a dimensionless number called the index of refraction c speed of light in vacuumnv speed of light in the medium= = .The speed of light in a vacuum, c, is an absolute maximum speed; thespeed of light in a medium is always less than c. So in a medium v < c , always n = c / v > 1, always.Last update: 1/13/2019 Dubson Phys1120 Notes, University of Colorado mirrorirmaterialindex nvacuum1 air1.0003 1water1.33Lucite1.51glass1.45 – 1.75diamond2.42sourcedeye"virtual image"dmirrorsourcedeye"virtual image"dTrick in analyzing mirror problems: redraw the incident / reflected rays as straight lines.dullshinyOptics-3When a ray of light passes from 1 medium to another, the ray is bent or refracted according to .. Snell's Law: 1 1 2 2n sin n sinq = qIn optics, angles are always measured with respectto the normal (perpendicular) direction.Notice that the ray is closer to the normal in themedium with the larger index n. The larger the change in n, the more the ray is bent. 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, thereare both reflected and refracted rays. 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 rayLast update: 1/13/2019 Dubson Phys1120 Notes, University of Colorado normalmedium 1medium 2interface12incidentn1n2 ( > n1 )reflectedrefracted < c = c > cn1 < n2n2no refracted rayOptics-4Example 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: 1 1 2 2ow c11 1 oc cw wn sin n sinn sin (1) sin(90 ) 11 1 1sin sin sin 48.8n n 1.33- -q = qq = =� �� ������q = � q = = =���������� �� �144424443 Light pipes guide light rays by total internal reflection.Last update: 1/13/2019 Dubson Phys1120 Notes, University of ColoradoOptics-5Lenses and image formationImages 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 parallelsurfaces), the incoming ray and the outgoing ray are parallel. Therefraction (ray bending) at the air/glass interface on the way in isexactly undone by the refraction at the glass/air interface on theway out.2) For a wedge-shaped piece of glass, like a prism, the ray is benttoward 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.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. Last update: 1/13/2019 Dubson Phys1120 Notes, University of Colorado parallel raysfocal pointfocal length f > 0short flong fair glass airOptics-6Parallel rays are produced by distant point sources light rays from a star in the sky are parallel. Diverging lens or concave lens: Thin in the middle, thick at theedges. Remember, rays bend towardthe thicker end. You can form images on a screen of distant objects using a converging lens.Last update: 1/13/2019 Dubson Phys1120 Notes, University of Colorado point sourcefar from source, small bundle of rays is nearly paralleltwo distant point sourceslensscreen12focalplaneffrom source 1from source 2parallel raysfocusfocal length f < 0Optics-7If the screen is placed at the focal plane of the lens (one focal length f away from the lens),
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