Lec. 6: Ch. 2 - Geometrical Optics

Transcription

1 Lec. 6: Ch. 2 - Geometrical Optics We are here 1. Shadows 2. Reflection 3. Refraction 4. Dispersion Guest lecture Tuesday, February 2, by Dr. Greg Werner. 1 Review Equal angle rule Similar triangles are useful for shadows θ i θ r Normal Mirror Ray tracing a mirror X object = X image Image point is on the normal (mirror might need an extension) X object Extension X image 2

2 Virtual image: (p. 73) The light appears to come from the virtual image, but in fact does not come from there. object virtual image Real image: (p. 84) The light comes to you from a real image. You may need a screen to see it, or ground glass. a real image: 3 Refraction 1. Index of refraction: n = c / v 2. Ray in water is closer to the normal 3. Total internal reflection 4. Mirages 4

3 What is refraction? Refraction is bending of a ray at a boundary due to a different speed of light in the substance. Air Air Water Water Demo: tank, laser pointer 5 Indices of refraction v = c / n Substance: Index of refraction n: Vacuum Air Water Glass 1.5 (depends on kind) Diamond 2.4 6

4 Optional math: Snell s law n 1 sin θ 1 = n 2 sin θ 2 θ 1 Air n 1 = θ 2 Water n 2 = Light coming out of water: 2 possibilities Total internal reflection is possible! Refracted Air Reflected internally Water The critical angle is about 42 degrees. Case 1 near normal incidence (light comes out) Case 2, far from normal incidence (internal reflection) Demo: tank, laser pointer 8

5 Total internal reflection seen by diver Refraction makes objects in water seem nearer to the surface

6 This illustration appears in "La Nature" magazine in Demo: tank 11 Total internal reflection makes fiber optic communication possible The ray bends from the low n material toward the high n material. Demo: glass tube, laser pointer 12

7 Fiber optics makes endoscopy possible polyp (precancer condition) [after age 50] 13 Lec. 6: Ch. 2 - Geometrical Optics We are here 1. Shadows 2. Reflection 3. Refraction 4. Dispersion 14

8 Dispersion Dispersion: refraction (bending) of different colors by different amounts. Spectrum Prism Light bulb 15 Index n varies with color Quartz glass wavelength n (index of refraction) 300 nm (UV) (bent more) 500 nm nm (deep red) (bent less) 16

9 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. 17 Rainbows: dispersion by water raindrops 180 degree rainbow is possible. Double rainbow is possible. Both together is very rare. 18

10 How we see a rainbow Sun (behind you) big raindrops this ray not seen these rays are seen this ray not seen 19 Pink Floyd 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

11 How we see two rainbows three total internal reflections sun two total internal reflections 21 Waterfall droplets create rainbows 22

12 23 (sun behind you) Fogbow (sun if front of you) Circles around the Moon also occur. 22 degrees, center to edge 24

13 Sun pillar and sun dogs 25 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 100 C. 26

14 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. 27 Superior mirage (image above the object) 28

15 29 The green flash at sunset is rare! Pekka Parvianen 30

16 Lec. 6: Ch. 2 - Geometrical Optics We are here 1. Shadows 2. Reflection 3. Refraction 4. Dispersion Move to Chap Lec. 6: Ch. 3 - Geometrical Optics We are here 1. Virtual images (review) 2. Spherical mirrors 3. Spherical lenses 4. Aberrations of lenses Guest lecture Tuesday, February 2, by Dr. Greg Werner. Skip 3.3c anamorphic art. 32

17 Virtual image: (p. 73) The light appears to come from the virtual image, but in fact does not come from there. 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 33 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. 34

18 Mirrors can be plane, convex or concave Convex traffic safety mirror Objects may be closer than they appear. 35 Mirrors can be plane, convex or concave Concave solar concentrator 36

19 Parabolic trough has curve in one direction only An alternative energy source in hot climates. The concentrated rays can boil water. These must be tilted up and down as the sun rises and sets. 37 Radio telescopes concentrate radio waves Before the accident After the accident 15 November, 1988 (Structural failure) 38

20 Web tutorials with Java Applets Useful web links on curved mirrors Useful web links on lenses