MOTION MOUNTAIN

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162 4 images and the eye – optics Ref. 126 Ref. 127 Challenge 170 s Challenge 171 d Challenge 172 s Ref. 128 Challenge 173 ny tionalantennas.Applications interahertztechnologymightalsoarise. Less serious workers in the field claim that invisibility cloaks can be realized with metamaterials. While this is a good marketing slogan to attract funding and get into newspapers, the dream is not realistic, due to inevitable signal losses in the materials, dispersion, refraction, finite cell size, the need for windows to observe the outside from inside and the impossibility to achieve invisibility for all wavelengths. So far, all aeroplanes that were claimed to be invisible even only for specific radar frequencies have turned out to be visible to radar after all. But sources of military funding are known to have only a distant relation to reality. Metamaterials for sound and lower-frequencywaves are also subject of research. Such acoustic or mechanical metamaterials have not found a technical application yet. Light around corners – diffraction Light goes around corners.This effect was calleddiffraction by Francesco Grimaldi, in his textPhysico-mathesisdelumine, published in 1665. Grimaldi studied shadows very carefully. He found out what everybody now learns in secondary school: light goes around corners in the same way that sound does, and light diffraction is due to the wave nature of light. (Newton got interested in optics after he read Grimaldi; Newton then wrongly dismissed Grimaldi’s conclusions.) Because of diffraction, it isimpossible to produce strictly parallel light beams. Forexample, every laser beam diverges by a certain minimum amount, called the diffraction limit. Maybe you know that the world’s most expensive Cat’s-eyes are on the Moon, wheretheyhave been deposited by the Lunokhod and the Apollo missions. Can youdetermine how wide a laser beam with minimum divergence has become when it arrives at the Moon and returns back to Earth, assuming that it was1m wide when it left Earth? How wide would it be on its return if it had been1 mm wide at the start? In short, both diffraction and the impossibility of non-diverging beams confirm that light is a wave. Diffraction implies that there are no perfectly sharp images: there exists a limit on resolution. This is true for every optical instrument, including the eye. The resolution of the eye is between one and two minutes of arc, i.e., between 0.3 and0.6 mrad. The limit is partly due to the finite size of the pupil. (That is why squinting helps to see more sharply.) In practice, the resolution of the eye is often limited by chromatic aberrations and shape imperfections of the cornea and lens. (Can you check the numbers and their interpretation by calculation? Is it true that the number of rods in the eye is tuned exactly to its resolution?)Therefore, for example, there is a maximum distance at which humans can distinguish the two headlights of a car. Can you estimate it? Resolution limits also make it impossible to see the Great Wall in northern China from the Moon, contrary to what is often claimed. In the few parts that are not yet in ruins, the wall is about 6 metres wide, and even if it casts a wide shadow during the morning or the evening, the angle it subtends is way below a second of arc, so that it is completely invisible to the human eye. In fact, three different cosmonauts who travelled to the Moon performed careful searches and confirmed that the claim is absurd. The story is one of the most tenacious urban legends. (Is it possible to see the Wall from the space shuttle?) The largest human-made objects are the polders of reclaimed land in the Netherlands;they are visible from outer space. So are most large cities as well as the highways in Belgium Motion Mountain – The Adventure of Physics copyright © Christoph Schiller June 1990–November 2015 free pdf file available at www.motionmountain.net
images – transporting light 163 Naive prediction Observation lamp circular plate screen with shadow Poisson’s spot F I G U R E 111 Shadows show that light is a wave: the naive expectation (left), neglecting the wave idea, and the actual observation (middle and right) of the shadow of a circular object (photo © Christopher Jones). F I G U R E 112 Examples of diffractive optics: a diffractive aspherical lens, the result shining a red laser through of a plastic sheet with a diffractive cross generator, and an acousto-optic modulator used to modulate laser beams that are transmitted through the built-in crystal (© Jenoptik, Wikimedia, Jeff Sherman). at night; their bright illumination makes them stand out clearly from the dark side of the Earth. Diffraction has the consequence that behind a small disc illuminated along its axis, the centre of the shadow shows, against all expectations, a bright spot, as shown in Figure111.This ‘hole’ intheshadowwaspredictedin1819byDenisPoisson(b.1781Pithiviers,d.1840Paris)in order to show to what absurd consequences the wave theory of light would lead. He had just read the mathematical description of diffraction developed by Augustin Fresnel* on the basis of the wave description of light. But shortly afterwards, François Arago actually observed Poisson’s spot, converting Poisson, making Fresnel famous and starting the general acceptance of the wave properties of light. Diffraction can also be used, in certain special applications, to produce images. A few examples of the use of diffraction in optics are shown in Figure 112. Of these, acousto- opticmodulatorsareusedinmanylasersystems,forexampleinlasershows.Alsoholo- *AugustinJean Fresnel(b.1788Broglie,d.1827Ville d’Avray),engineer andpart time physicist.The ‘s’ in his name is silent. In 1818, he published his great paper on wave theory for which he got the prize of the FrenchAcademyofSciencesin1819.Toimprovehisfinances,heworkedinthecommissionresponsiblefor lighthouses,forwhichhedevelopedthewell-knownFresnellens.Hediedprematurely,partlyofexhaustion duetooverwork. Motion Mountain – The Adventure of Physics copyright © Christoph Schiller June 1990–November 2015 free pdf file available at www.motionmountain.net
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ChristophSchiller MOTION MOUNTAIN t
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Editiovicesima octava. Proprietassc
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DieMenschenstärken,die Sachenklär
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8 preface PHYSICS: Describing motio
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10 preface Your donation to the cha
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12 contents Do we see what exists?
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Light, Charges and Brains Inourques
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16 1 electricity and fields F I G U
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44 1 electricity and fields Vol. IV
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Chapter 3 WHAT IS LIGHT? Ref. 57 Pa
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110 3 what is light? incoming light
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248 7 the story of the brain Vol. I
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254 7 the story of the brain ∗∗
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Chapter 8 THOUGHT AND LANGUAGE Ref.
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CREDITS Acknowledgements Many peopl
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NAME INDEX A Abbott A Abbott,T.A.37
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406 subject index A units 328 Aplys
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