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). Mirrors When light reflects from a dull surface, the rays scatter in all directions, so observers can see reflected rays from all directions. 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 θ i = θ r Why does the light reflected from a smooth surface scatter in one direction only? When you study speed c aperture diameter Dsource beam or ray of light if D >> λ λ eyelight ray eyedull surfacemirrorθr θi Last update: 11/16/2009 Dubson Phys1120 Notes, ©University of ColoradoOptics-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 θ i = θ f . Any surface is shiny and mirror-like if it is smooth compared to the wavelength of light λvisible ≈ 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 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 Law Any 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; the speed of light in a medium is always less than c. So in a medium v < c , always ⇒ n = c / v > 1, always. material index n vacuum 1 air 1.0003 ≅ 1 water 1.33 Lucite 1.51 glass 1.45 – 1.75diamond 2.42 sourcedeye "virtual image" dmirror dull shiny λ λ Last update: 11/16/2009 Dubson Phys1120 Notes, ©University of ColoradoOptics-3 When a ray of light passes from 1 medium to another, the ray is bent or refracted according to .. Snell's Law: 11 2 2nsin nsinθ = θIn optics, angles are always measured with respect to the normal (perpendicular) direction. medium 1 medium 2Notice that the ray is closer to the normal in the medium 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, there are 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 raynormalinterface θ1 θ2 n1 reflectedincidentn2 ( > n1 ) refractedθ < θc θ = θc no refracted rayn1 < n2 n2 θ > θc Last update: 11/16/2009 Dubson Phys1120 Notes, ©University of ColoradoOptics-4 Example of total internal reflection. What is the critical angle θc 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: 11 2 2owc111ccwwn sin n sinn sin (1) sin(90 ) 1111sin sin sin 48.8n n 1.33−−θ = θθ ==⎛⎞⎛⎞⎟⎜⎟⎜⎟θ = ⇒θ== =⎜⎟⎜⎟⎟⎜⎜⎟⎜⎝⎠⎝⎠o Light pipes guide light rays by total internal reflection. Last update: 11/16/2009 Dubson Phys1120 Notes, ©University of ColoradoOptics-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: air glass air 1) For a ray passing through a flat plate of glass (with parallel 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 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. parallel raysfocal length f > 0short flong fLast update: 11/16/2009 Dubson Phys1120 Notes, ©University of ColoradoOptics-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 point sourceis nearly parallel Diverging lens or concave lens: parallel raysThin in the middle, thick at the edges. Remember, rays bend toward the thicker end. focusfocal length f < 0 You can form images on a screen of distant objects using a converging lens. two distant point sourceslensscreen12focal from fsource 1from source 2planeLast update: 11/16/2009 Dubson Phys1120 Notes, ©University of ColoradoOptics-7 If the screen is placed at the focal plane of the lens (one focal length f away from the
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