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class24lecnotes - NOI1t1t1Aj ~ l4)n,h./O/i5S Zr sO>0 Z...

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NOI1t1t1Aj ~ l4()n:,h :;, .«(}/O [(/i5S Zr,. , sO./ ,>0. Z Geometrical Optics .+ . ( Humans have always been fascinated by light and attempted to explain its nature. As it is usually the case with things we take for granted, they tum out to be most intriguing upon deeper examination. QuestiollSlike "How do we see light?" or "How do we see objec~" are worth more than a passing thought. Our modem understanding to the questions above is that something enters the eye . i, after bouncing off an object. This stands in stark contrast to the ancient view by which must flow out of the eye and sleepwalk toward the object that is to be seen. Everyday experience reveals that light travels in straight lines until it meets an obstacle. Most interestingly, light rays can cross path without affecting each other. As they do this, the information they carry is not altered. This observation was, in fact, a powerful argument against the corpuscular nature of light pushed forward by Newton. When we study light as a ray we operate within the geometric optics approximation. What is its range of validity? In an earlier class we explored the validity of the wave optics in the context of visible light. Over the past weeks of class we learned that when light passes through sufficiently small openings, it spreads (diffraction). We worked out the angle under which we see the first minimum of diffraction JI"r a;:;1/ a. pr tf, .::: 1- ~r A ~ and the width of the central maximum /AI::: 2. '-j !/ A ~~ a.. The quantity lJa (a is the width of the slit) determines how much the wave spreads. By contrast, when ~a, there is no visible spreading. The width of the central maximum becomesa. For a circular aperture of diameter a, the angle of the first minimum can be derived as: ~ ~ = It2 ~ tA. And the width of the central maximum becomes: W'o: t,y AL (/L
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When w=a, we transition from the wave optics regime to the geometrical optics approximation: /.~rl'L ::: a.. So, the geometrical optics approximation holds when a ~ /2,'1'1 AL For light with a wavelength of 500 nm, this leads to an aperture of (L .1 hi ) " () ::: jz.yy. fl()'lo-1 m , 1m -' /1'Hn-t Indeed, all optical instruments involved in geometrical optics have dimensions larger than 1 mm! In both the geometrical optics and the wave optics regime, the energy of the photons is low compared to the energy sensitivity of the equipment. In conclusion, in the geometric optics approximation, which holds for "-<<a: Light travels in straight lines between two points Beams of light intersect without consequences. -I. f{.ql~ll!J. Sr~ A modern visualization of these ideas are laser beams . .Aft interesting addition: (y ou~;;-- only see their light if they scatter off dust along their path, Their light is made visible by its interaction with the medium through which it propagates. An application of these ideas is the pinhole camera. In a dark room, light is allowed to enter through a small opening, On the far wall of this room, you can see an upside down projection of the outside world. The image is fairly dim, as most of the light coming from the objects (in this case a tree), does not enter the box,
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class24lecnotes - NOI1t1t1Aj ~ l4)n,h./O/i5S Zr sO>0 Z...

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