23-1 (SJP, Phys 2020, Sp ‘09) Light and Optics: We just learned that light is a wave (an "electromagnetic wave", with very small wavelength). But in many cases, you can safely ignore the wave nature of light! Light was studied for a long time (obviously), long before Mr. Maxwell, and very well understood. People thought about light as sort of like a stream of "particles" that travel in straight lines (called "light rays"). Unlike particles, waves behave in funny ways - e.g. they bend around corners. (Think of sound coming through a doorway.) But, the smaller the λ is, the weaker these funny effects are, so for light (tiny λ), no one noticed the "wave nature" at all, for a long time. λ of light is 100 x's smaller than the diameter of a human hair! We'll come back to the (subtle) wave nature of light in Ch. 24. But for now, we'll study the more "classical" aspects, called GEOMETRICAL OPTICS - the study of how light travels, and how we perceive and manipulate it with mirrors and lenses. We'll also be incorporating parts of CH. 25 into this as we go along, because Ch. 25 is about lenses, glasses, telescopes, etc. • We will ignore time oscillations/variations (10^14 Hz is too fast to notice!) • We'll assume light travels in straight lines (c=3E8 m/s, super fast) • Light can then change directions in 3 main ways: i) Bouncing off objects = reflection ii) Entering objects (e.g. glass) and bending = refraction iii) Getting caught, and heating the object = absorption ( iv) Bending around objects = diffraction is a subject for Ch. 24)23-2 (SJP, Phys 2020, Sp ‘09) How do you know where objects are? How do you see them? You deduce the location (distance and direction) in complicated physiological/ psychological ways, but it arises from the angle and intensity of the little "bundle" of light rays that make it into your eye. If light bounces off a smooth surface (like a mirror, or a lake), it's called "specular reflection", and it is always true that Θ(i) = Θ(r), "angle of incidence"="angle of reflection" (See sketch for the precise definition of which angles those are!) If light bounces off a dull surface (like e.g. white paper, or a wall), it's called "diffuse reflection", and the light comes out every which way. (Microscopically, "dull" means that the surface is not smooth on the scale of the wavelength of light) (Only those in this "bundle" reach eye) (Many rays leave) "normal" light out ("reflected") light in ("incident") mirror! r! i out in in in in in out out out out out out in in in23-3 (SJP, Phys 2020, Sp ‘09) If rays come from a "point source" (a small bulb, the tip of my noise, the end of an arrow, ...a particular point on an object) and then reflect off a mirror, they will appear to come from behind the mirror (to an observer properly located): My eye sees (some of) the rays leaving the object. My brain assumes they rays must have travelled straight, so my brain "draws the dashed lines" and deduces the object must be located at the "image point" shown on the right. This image is called virtual. The rays appear (to me) to come from that point in space, but they were never really there! (If you put a piece of paper somewhere back there blocking the dashed lines, it has no effect on the image. The paper is behind the mirror, after all!) We'll encounter "real images" soon like the image projected onto a movie screen. But you don't get that with a simple flat mirror - as you can see above, the image is virtual. • Note: many rays go from the object "o" to the eye. You can show (see Giancoli P. 686) that they all appear to come from the same image point. I only drew 2 of those rays, to keep the picture as simple as possible. (All you need is two lines, in general, to trace back to a unique point origin) • The distance "d" in the picture above is the same for both object and image. If an object is 2 m in front of the mirror, I will perceive it to be 2 m behind the mirror (a total of 4 m horizontally away from the object) • Curved mirrors can play nice tricks on you! ("Object in mirror is farther than it appears") Depending on the shape, images can appear closer, farther, bigger, smaller... (Giancoli section 23-3 is about this: it's fun, but optional reading) Only rays in this bundle reach eye via mirror perceived (virtual) image mirror object (pt. source) d d23-4 (SJP, Phys 2020, Sp ‘09) Any transparent medium (air, H20, glass,...) that lets light through will have a number n, the "index of refraction", associated with it. n is determined by how fast light travels through the material. (Light only travels at c, the "speed of light", in vacuum. In materials, it is always slowed down.) The bigger n, the slower the light travels: n = c/v = speed of light (in vacuum) / speed of light (in medium) = 3E8 m/s / v (in medium) n >1 always. (another way to say this: light never goes faster than c!) Examples: air: n= 1.0003 water: n=1.33 glass: n=1.5 diamond: n=2.4 (light travels less than half the normal speed in diamond!) Over in the JILA labs, there are experiments with materials that have n (at one special frequency, anyway) about 1E7, so large that the speed of light is about as slow as a person on a bike! If light goes from one medium into another, it will (in general) bend, i.e. change it direction. This is called refraction. This fact is explained way back in Giancoli 11-13: it is a property of waves. Nevertheless, the description of the effect doesn't need to refer to the wavelength, or wave nature, of light, so this topic still belongs in this geometrical optics chapter. The math involved is fairly straightforward (one equation to learn), and there are many important consequences/applications, ragning from simple eyeglass lenses, to fancy telescopoes, to medical imaging equipment, optical fibers for phone lines, etc...23-5 (SJP, Phys 2020, Sp ‘09) • Light is SLOWER on the right side, where n2 is large. • θ1 is larger, θ2 is smaller: Light gets bent "towards the normal" as it goes from low index (like air) into higher index (like glass) (And vice versa = you can always reverse a ray diagram like this) There is a formula for the refraction of light (as shown in this figure) derivable from Maxwell's Equations, called Snell's Law: n1 sin(θ1) = n2 sin(θ2). (See fig for definitions of symbols) Example: You are looking into
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