Lec. 7: Ch. 2 - Geometrical Optics. 1. Shadows 2. Reflection 3. Refraction 4. Dispersion. 5. Mirages, sun dogs, etc.

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1 Lec. 7: h. 2 - Geometrical Optics We are here 1. Shadows 2. Reflection 3. Refraction 4. Dispersion We only covered the first 44 vugraphs. 5. Mirages, sun dogs, etc. Read hapter 3, skip 3.3 and skip 3.5D Skip solar power, pp Dispersion Dispersion: refraction (bending) of different colors by different amounts. Spectrum Prism Light bulb 2

2 Index n varies with color Quartz glass wavelength n (index of refraction) 300 nm (UV) (bent more) 500 nm nm (deep red) (bent less) 3 Prisms demonstrate refraction and dispersion Reflection at a transparent surface occurs because the n values are different. Only a few percent of the light is reflected this way. 4

3 Rainbows: dispersion by water raindrops 180 degree rainbow is possible. Double rainbow is possible. Both together is very rare. 5 How we see a rainbow Sun (behind you) big raindrops this ray not seen these rays are seen this ray not seen 6

4 Pink loyd is slightly wrong. The colors are spread inside the prism as well as outside. The colors start to spread inside the raindrop. Dispersion occurs here during refraction white light comes in Reflections Raindrop Dispersion occurs here during refraction A spectrum of colors comes out Animated slide 7 How we see two rainbows two total internal reflections sun two total internal reflections 8

5 9 Waterfall droplets create rainbows 10

6 11 Lec. 7: h. 2 - Geometrical Optics 1. Shadows 2. Reflection 3. Refraction 4. Dispersion We are here 5. Mirages, sun dogs, etc. 12

7 (sun behind you) ogbow (sun if front of you) ircles around the Moon also occur. 22 degrees, center to edge degree halo You only see the purple rays 14

8 Sun pillar and sun dogs 15 What is a mirage? A mirage is an image (often upside down) caused by heated air refracting rays. n falls from at room temperature to when the temperature goes up

9 Inferior mirage (image below the object) sky appears to be on the ground The ray bends from the low n material toward the high n material. 17 Superior mirage (image above the object) 18

10 19 The green flash from dispersion at sunset is rare! Pekka Parvianen 20

11 Lec. 6: h. 3 - Geometrical Optics We are here 1. Virtual images (review) 2. Spherical mirrors 3. Spherical lenses 4. Aberrations of lenses 21 Virtual image: (p. 73) The light appears to come from the virtual image, but in fact does not come from there, it comes from a lens or mirror. object Real image: (p. 84) The light comes to you from a real image. You may need a screen to see it. a real image: virtual image 22

12 Mirrors and lenses We will study these two cases. A positive lens is thicker in the middle. A negative lens is thicker at the edge. 23 Mirrors can be plane, convex or concave onvex traffic safety mirror, similar to anti-shoplifting mirror. Objects may be closer than they appear. 24

13 Mirrors can be plane, convex or concave oncave solar concentrator 25 Lec. 7: h. 3 - Geometrical Optics We are here 1. Virtual images (review) 2. Spherical mirrors 3. Spherical lenses 4. Aberrations of lenses 26

14 This line segment (from center of circle)... urved Mirrors irst, a little geometry review:...is perpendicular (or normal) to this tangent. We use a circle to represent a spherical surface. 27 Rays reflecting from a convex (spherical) mirror Ray aimed toward center of sphere comes straight back (specular reflection with normal incidence) What about other rays? Ray reflects at the surface This is rule 2. All rays aimed at the center come straight back out. is also called center of curvature. 28

15 What happens to all rays that come in parallel? Specular reflection ind where incoming ray hits mirror surface ind surface normal at that point Angle of incidence = angle of reflection Reflection (of parallel ray) looks like it s coming from -- turns out this is true for all parallel rays. θ i θ r No light is actually back here The focus is halfway to the center 29 What happens to all rays that come in parallel? ocal point = focus is behind the surface Easy rule for parallel incoming rays (parallel to the line between and ): they are reflected as if they came from. This is rule 1. The focus is halfway to the center 30

16 What about rays aimed at the focus? (This is the previous rule, backwards) Easy rule 3 for rays aimed at focus: An incoming ray aimed at gets reflected back parallel (to the - axis). ocal point = focus is behind the surface The focus is behind and halfway to the center Rule 3 is rule 1 backwards. 31 Three easy rules for convex, spherical mirrors 1. All rays incident parallel to the - axis are reflected so that they appear to be coming from the focal point 2. All rays that (when extended) pass through the center are reflected back on themselves. 3. All rays that (when extended) pass through the focal point are reflected back parallel to the axis

17 Ray tracing: convex mirror using the 3 rules Hint: start the rays moving toward the mirror and these rays must contain the arrow head. Questions: Is the image real or virtual? Is the image larger or smaller than the object? Is the image right-side-up or upside-down? Demo with vugraph machine and pens 33 Ray tracing: convex mirror object image Questions: Is the image real or virtual? Is the image larger or smaller than the object? Is the image right-side-up or upside-down? How could a mirror be useful when used like this? 34

18 Rays reflecting from concave (cavity) mirrors Ray through the center reflects straight back at its source Rule 2 applied to concave mirrors 35 Incoming parallel rays reflect through the focus All incoming parallel rays reflect and go through the focus, about half way from center to mirror This is rule 1. As usual, this rule 1 works backwards: incoming rays that go through the focus reflect back parallel (to the - axis) and this is rule

19 Rays through focus reflect back parallel to - axis. 37 Three easy rules for concave, spherical mirrors 1. All rays incident parallel to the - axis are reflected through the focal point 2. All rays that pass through the center are reflected back on themselves. 3. All rays that pass through the focal point are reflected back parallel to the axis

20 oncave mirrors are very useful light beam emitter (flashlight) light collector or solar oven 39 Ray tracing: concave mirror object outside center ase 1 Hint: start the rays moving toward the mirror and these rays must contain the arrow head. Demo with vugraph machine and pens 40

21 Ray tracing: concave mirror object outside center ase 1 I could switch the labels on the object and image and the drawing is still right! Questions: Is the image real or virtual? Is the image larger or smaller than the object? Is the image right-side-up or upside-down? How could a mirror be useful when used like this? 41 Ray tracing: concave mirror object between center and focus ase 2 Hint: start the rays moving toward the mirror and these rays must contain the arrow head. Questions: Is the image real or virtual? Is the image larger or smaller than the object? Is the image right-side-up or upside-down? How could a mirror be useful when used like this? 42

22 Ray tracing: concave mirror object between focus and mirror ase 3 43 Ray tracing: concave mirror object between focus and mirror Questions: Is the image real or virtual? Is the image larger or smaller than the object? Is the image right-side-up or upside-down? How could a mirror be useful when used like this? 44

23 Web tutorials with Java Applets Useful web links on curved mirrors Useful web links on lenses We now have many distinct cases onvex spherical mirror object outside only oncave spherical mirror, object outside center oncave spherical mirror, object between center and focus oncave spherical mirror, object between focus and mirror or each case, you can now answer: Image larger? Virtual? Where? What good is it? AND you can answer these question by ray tracing with three simple rules 46

24 On to lenses: first, review refraction air n=1 (nearly) v = c (nearly) glass, e.g. n=1.5 v = c/n < c Rays bend toward normal when entering slower medium (larger n), away from normal when entering faster medium (smaller n). 47 A trick to remember which way rays bend Soldiers in mud analogy (challenge: where does this analogy break down?) As soldiers slow down, space between them narrows rays (perpendicular to fronts) pavement (soldiers go fast) fronts deep mud (soldiers march slower through deep mud) 48

25 Ray tracing with lenses Brute force ray tracing: n=1 n>1 1. As long as ray stays in same medium, it goes straight. 2. At each interface to a different medium, use Snell s law to calculate how it will bend. Go back to 1. This gets tedious! Rays entering slower material bend toward normal Rays entering faster material bend away from normal 49 Thin convex (converging) lens focal length foci 50

26 Thin convex lens: three easy rules for ray tracing 1) A ray parallel to the axis is deflected through the focus on the other side 2) A ray through the center of the lens continues undeviated 3) A ray come from the focus on one side goes out parallel to the axis on the other 1 focal length foci 51 Ray might have to be extended Note light-focusing property of convex (converging) lens a good light collector or solar oven; can also fry ants with sunlight, but please don t do that unless you re going to eat them 52

27 Note light-dispersing property of convex lens The backwards light collector: create a collimated light beam 53 Where will this ray go? Ray Tracing foci (focuses?) 54

28 Where will this ray go? Suppose it s emitted from this object Ray Tracing foci (focuses?) Where will this ray go? Suppose it s emitted from this object Ray Tracing We know where these 3 rays go, using the simple ray rules foci (focuses?) 56

29 Where will this ray go? Suppose it s emitted from this object Ray Tracing Amazing property of this lens: all rays from the object will converge to the same point We know where these 3 rays go, using the simple ray rules foci (focuses?) 57 Ray Tracing Where will this ray go? Suppose it s emitted from this object Amazing property of this lens: all rays from the object will converge to the same point We know where these 3 rays go, using the simple ray rules foci (focuses?) 58

30 Ray Tracing: thin lens, object outside focus Amazing property of this lens: all rays from the object will converge to the same point (the image) See how the rays emerge from this point (the image)? 59 Thin concave (diverging) lens Guess how this ray will be bent: or diverging lens focal length defined to be negative (of the distance between focus and lens) 60

31 Thin concave (diverging) lens or diverging lens focal length defined to be negative 61 Thin concave (diverging) lens: three easy ray rules 1) A ray parallel to the axis is deflected as if it came from the focus 2) A ray through the center of the lens continues undeviated 3) A ray aimed at the focus on the other side comes out parallel Ray might have to be extended or diverging lens focal length defined to be negative 62

32 Difference between convex (converging) and concave (diverging) lenses 1 (Rule 3, the backwards version of rule 1, also differs) 1 63 Ray tracing a convex lens: object inside focus 64

33 Ray tracing a convex lens: object inside focus The image appears larger (and farther away) than the object. This is a magnifying glass. (Remember: a magnifying glass is a convex lens.) Aside: near-sighted people need concave/diverging lenses; can a marooned myopic start a fire with his eye-glasses? 65 onvex lens ray tracing: 3 cases Like concave mirrors, convex lenses have 3 kinds of cases for ray tracing: 1. object inside focal length 2. object outside focal length, inside twice focal length 3. object outside twice focal length You can do the ray tracing and answer the following questions: Is the image real/virtual? Is the image larger/smaller than the object? Is the image erect/inverted? How can the lens be used? 66