0 n2 15 note that the wheels move faster bigger space

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Unformatted text preview: erwater…) incoming ray hugs surface UCSD: Physics 121; 2008 Refraction in Suburbia – wheel moves slower in grass, so the direction changes n1 = 1.0 n2 = 1.5 Note that the wheels move faster (bigger space) on the sidewalk, slower (closer) in the grass 42° Winter 2008 9 Winter 2008 10 UCSD: Physics 121; 2008 UCSD: Physics 121; 2008 Even gets Total Internal Reflection Right • Moreover, this analogy is mathematically equivalent to the actual refraction phenomenon – can recover Snell’s law: n 1sin 1 = n2sin Reflections, Refractive offset • Let’s consider a thick piece of glass (n = 1.5), and the Let’ 1.5), light paths associated with it 2 – reflection fraction = [(n1 – n2)/(n1 + n2)]2 – using n1 = 1.5, n2 = 1.0 (air), R = (0.5/2.5)2 = 0.04 = 4% n1 = 1.5 n2 = 1.0 incoming ray (100%) 96% image looks displaced due to jog 8% reflected in two reflections (front & back) Wheel that hits sidewalk starts to go faster, which turns the axle, until the upper wheel re-enters the grass and goes straight again 4% 92% transmitted 4% Winter 2008 Lecture 6 11 Winter 2008 0.16% 12 3 Geometrical Optics 01/31/2008 UCSD: Physics 121; 2008 UCSD: Physics 121; 2008 Cameras, in brief Let’s get focused… Let’ focused… • Just as with mirrors, curved lenses follow same rules as flat interfaces, using local surface normal local surface A lens, with front and back curved surfaces, bends light twice, each diverting incoming ray towards centerline. Follows laws of refraction at each surface. Parallel rays, coming, for instance from a specific direction (like a distant bird) are focused by a convex (positive) lens to a focal point. pinhole object image at film plane In a pinhole camera, the hole is so small that light hitting any particular point on the film plane must have come from a particular direction outside the camera object image at film plane lens Placing film at this point would record an image of the distant bird at a very specific spot on the film. Lenses map incoming angles into positions in the focal plane. Winter 2008 13 In a camera with a lens, the same applies: that a point on the film plane more-or-less corresponds to a direction outside the camera. Lenses have the important advantage of collecting more light than the pinhole admits Winter 2008 14 UCSD: Physics 121; 2008 UCSD: Physics 121; 2008 Positive Lenses Negative Lenses • Thicker in middle • Bend rays toward axis toward axis • Form real focus real focus Winter 2008 Lecture 6 • Thinner in middle • Bend rays toward axis toward axis • Form virtual focus virtual focus 15 Winter 2008 16 4 Geometrical Optics 01/31/2008 UCSD: Physics 121; 2008 UCSD: Physics 121; 2008 Raytracing made easier Thin Lens Benefits • In principle, to trace a ray, one must calculate the intersection of each ray with the complex lens surface, compute the surface normal here, then propagate to the next surface • If the lens is thin, we can say that a ray through the lens center is undeflected undeflected – real story not far from this, in fact: direction almost identical, just a jog – the jog gets smaller as the lens gets thinner – computationally very cumbersome • We can make things easy on ourselves by making the following assumptions: – all rays are in the plane (2-d) – each lens is thin: height does not change across lens – each lens has a focal length (real or virtual) that is the same in both directions Winter 2008 17 Winter 2008 UCSD: Physics 121; 2008...
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