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Brilliant-Cut Diamonds and Other Tricks of the Light

Brilliant-Cut Diamonds and Other Tricks of the Light. John D Barrow. Diamond Geezer. Marcel Tolkowsky (1899-1991) Diamond Design: A study of the reflection and refraction of light in a diamond , E & F.N. Spon, Ltd., London, 1919, while a graduate student at Imperial College.

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Brilliant-Cut Diamonds and Other Tricks of the Light

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  1. Brilliant-Cut Diamonds and Other Tricks of the Light John D Barrow

  2. Diamond Geezer Marcel Tolkowsky (1899-1991) Diamond Design: A study of the reflection and refraction of light in a diamond, E & F.N. Spon, Ltd., London, 1919, while a graduate student at Imperial College

  3. Old Diamond Cuts Stylistic evolution from the most primitive (Point Cut) to the most advanced pre-Tolkowsky cut (Old European)

  4. Brilliant Cut Diamonds MT: “We have therefore to study these optical properties in order to be able to apply them to the problem we have now before us :  the calculation of the shape and proportions of a perfectly cut diamond.”

  5. Reflection of Light A B a a mirror C Minimises the time to traverse A  C  B

  6. The Maths of Baywatch lifeguard beach shoreline sea swimmer is the least time path

  7. Refraction of Light n = sin(θ1)/sin(θ2) = (speed in medium 1)/(speed in medium 2) The least time path

  8. A Fish-eye View Critical angle for air-water interface is sin-1(1.00/1.33) = 48.8 deg

  9. n(diamond) = sin(i)/sin(r) = (speed in vacuum)/speed in diamond) n(diamond) = sin(iair)/sin(rdiamond) = 2.42 Critical angle with air = sin-1(1/n) n(air) = 1.0003  1 , n(water) = 1.33, n(glass) = 1.52 Crit(diamond) = 24.4 deg, Crit(glass) = 42 deg, Crit(water) = 48.8 deg Light speed in vacuum = 186,282 miles/second = 3 x 108 m/sec Light speed in diamond = 77,056 miles/second = 1.24 x108 m/sec

  10. Any ray which strikes the inside surface on the at an angle greaterthan 24.4 degrees will not escape the diamond.

  11. ‘Fire’ from Dispersion

  12. Pink Floyd: Dark Side of the Moon 1973 1993 2003

  13. Dispersion is also very large “Fire”

  14. The ‘Goldilocks’ Design Pavilion 40.75 deg Crown 34.5 deg Table Ratio 53%

  15. “For absolute total reflection to occur at the first facet, the inclined facets must make an angle of not less that 48°52' with the horizontal.” “For absolute total reflection at the second facet, the inclined facets must make an angle of not more than 43°43' with the horizontal.” “For[outgoing]refraction,  may be less or more than 45°. When more, the best value is 49°15', but it is unsatisfactory. When less, the best value is 40°45', and is very satisfactory, as the light can be arranged to leave with the best possible dispersion.” “Upon consideration of the above results, we conclude that the correct value for  is 40°45', and gives the most vivid fire and the greatest brilliancy, and that although a greater angle would give better reflection, this would not compensate for the loss due to the corresponding reduction in dispersion. In all future work upon the modern brilliant we will therefore take  = 40°45'. “ Marcel Tolkowsky, 1919

  16. OctNus: Sergey Sivovolenko, Yuri Shelementiev (2002)

  17. OctNus; Sergey Sivovolenko, Yuri Shelementiev (2002)

  18. Mirror, Mirror on the Wall

  19. Mirror, Mirror on the Wall

  20. Tarnowski Alter Ego Magritte

  21. John Barrow John Barrow NOT John Barrow OR John Barrow

  22. Through the Looking Glass

  23. Angled Mirrors 45 45 30 30 60 No right-left reversal in right-angled mirrors Reduce the angle and left-right reversal occurs at 60 degrees

  24. What do you really look like? 2 lefts vs 2 rights

  25. How big do you need to make a mirror ? How big does a mirror have to be, so that you can see all of your face in it ?

  26. Angle of incidence equals angle of reflection. Whatever the distance of the viewer, light from the top of the head is reflected from the mirror at a point half-way between the top or bottom of the head and the eyes. The mirror size is half the height of your head. The size of reflected image is the same no matter how far you are from the image

  27. a a a b b b Face size = 2a +2 b Mirror image size = a + b

  28. ‘Invisible’ Objects At least 4 reflections needed

  29. Pepper’s Ghost Invented by Henry Dircks and used by John Pepper, 1862

  30. The Optics of Pepper’s Ghost

  31. Gradually raise the lights in the darkened room on the left and the ghost appears

  32. Thomas Tobin’s Proteus CabinetLondon Polytechnic Institution,1865 “Here, but not Here” Safe zone 45 deg The first magic cabinet trick The first trick “all done with mirrors” Look

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