OPAC 202 Optical Design and Instrumentation Topic 3 Review Of Geometrical and Wave Optics Department of http://www.gantep.edu.tr/~bingul/opac202 Optical & Acustical Engineering Gaziantep University Feb 2018 Sayfa 1
Content Light Photometry Reflection and Refraction Prisims Mirrors Lenses Dispersion Polarization Interference and Diffraction Airy Disk Sayfa 2
R. Feynman, Lecture notes on Physics, Volume I, Chapter 37 Newton thought that light was made up of particles, but then it was discovered, that it behaves like a wave. Later, however it was found that light did indeed sometimes behave like a particle. Historically, the electron, for example, was thought to behave like a particle, and then it was found that in many respects it behaved like a wave. So it really behaves like neither. Now we have given up. We say: It is like neither. Richard Feynman Sayfa 3
Light Light is the portion of electromagnetic radiation that is visible to the human eye and is an energy propagating in space as photons. Experiments show that Light behaves like waves in its propagation and in the phenomena of interference and diffraction; However, it exhibits particle-like behavior when exchanging energy with matter, as in the Compton and photoelectric effects. Sayfa 4
Huygen s Principle In 1678, C. Huygens proposed a wave theory of light. He believed that light was a wave and that this wave was propagated through a material called the 'aether'. Since light can pass through a vacuum and travels very fast Huygens had to propose some rather strange properties for the aether: for example; it must fill all space and be weightless and invisible. For this reason scientists were sceptical of his theory. He proposed that every point to which a luminous disturbance reaches becomes a source of a spherical wave; the sum of these secondary waves determines the form of the wave at any subsequent time. Sayfa 5
Huygens Principle Sayfa 6
Light Waves In 1800, Thomas Young made the double-slit experiment İn which an opaque screen with two small, closely spaced openings was illuminated by monochromatic light from a small light source. The shadows observed are a complex interference pattern like those produced with water waves. Sayfa 7
Electromagnetic Waves James Clerk Maxwell first theoretically postulated EMWs (in 1862). These were confirmed by Heinrich Hertz experimentally (in 1886). Light is an electromagnetic wave that is visible to the human eye Sayfa 8
EMW in charge-free and current-free medium (ρ=0, J=0) Sayfa 9
EMW production EMWs are made up of time-varying electric and magnetic fields EMWs are produced by accelerating charges. Sayfa 10
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Quantum Theory of Light In 1900, Max Planck was used the idea that hot object emit light only as discrete packets of energy called photons. Energy of photon is given by: E h hc h is the Planck s Constant (h = 6.6 x 10 34 J.s) c is the speed of light The photon idea is later used by Einstein and Compton. a wave packet Light is an energy propagating in space as particles Sayfa 12
Photon 1905 Photoelectric Effect (A.Einstein) Kinetic energy of the ejected electron: K h w 1923 Compton Scattering (H.Compton) Wavelength of the scattered photon: ' h mec [1 cos ] Sayfa 13
Photon (rest mass, m = 0) The energy of a photon is not a function of its speed but rather of its wavelength. E hf p E c h p hc hc E Energy of the photon: Momentum of the photon Wavelength v c 3 10 8 m/s The speed of a photon in vacuum. Sayfa 14
Radiomery and Photometry In optics, the electromagnetic radiation measurement is studied in two groups: Radiometry is the measurement of optical radiation including visible light Photometry is the measurement of visible light only. Sayfa 15
Radiometry and Photometry Conversion The radiant power at each wavelength is weighted by a luminosity function V(λ) that models human brightness sensitivity. Conversion from power in Watt to power in Lumen: For Mono-chromatic light: v (683 lm/w) V ( ) For Poly-chromatic light: v (683 lm/w) ( ) V ( ) d 0 Sayfa 16
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Refraction Refraction is the change in direction of a ray due to a change in its transmission medium. Snell s Law of refraction: n 1 sin 1 n2 sin 2 Sayfa 18
Optical Slab A flat piece of glass can be used to displace a light ray laterally without changing its direction. When a light beam passes from air to a medium whose index is n and thickness h, then the incident beam will be deflected (shifted) by the offset d given by: where θ is the angle of incidence. Sayfa 19
Optical Slab Note that if θ is small then: Sayfa 20
Total Internal Reflection (TIR) TIR happens when a ray strikes a medium boundary at an angle larger than a particular critical angle given by: sin n c 2 / n 1 TIRs in a block of acrylic ==> Sayfa 21
Prism Transparent medium between two planes is called a prism Sayfa 22
Prisms I D 1 A 2 D 1 2 2 1/ 2 1 sin [( n sin 1) sin A cos Asin 1] A n sin[( A Dmin ) / sin[ A/ 2] 2] Sayfa 23
Some Reflecting Prisms Dove Prism Penta Prism Sayfa 24
Mirrors Plane Mirror and Diffuse Reflection Sayfa 25
Concave and Convex mirror: f = R / 2 where R is the radius of curvature of the mirror. Sayfa 26
Lenses Thin lens in air: 1 f ( n 1)[ 1 1 R 1 R 2 ] Thick lens in air (This is effective focal length in Zemax) 1 f ( n 1)[ 1 R 1 R ( n 1) t nr 1 2 1R2 ] Power of a lens: P 1 f Sayfa 27
Thin Lens Equivalent Pictures Sayfa 28
Various Lens Shapes Sayfa 29
Polarization Polarization is a property of certain types of waves that describes the orientation of their oscillations. Only transverse waves have polarization effect (e.g EMWs, GWs) Polarization can be obtained from an unpolarized beam by Selective absorption by Reflection by Scattering Sayfa 30
Interference and Diffraction Sayfa 31
Diffraction in a circular aperture Sayfa 32
Airy Disk When light passes through any size aperture (every lens has a finite aperture), diffraction occurs. The resulting diffraction pattern, a bright region in the center together with a series of concentric rings of decreasing intensity around it is called the Airy Disk. Sayfa 33
Airy Disk image of a point is not a point due to wave nature of light. Sayfa 34
Airy Disk The diameter of this pattern is related to the wavelength (λ) of the illuminating light and the size of the circular aperture, which is important since the Airy Disk is the smallest point to which a beam of light can be focused. Minimum spot size = Airy disk diameter is D airy 2.44 ( f /# ) where f/# = f/d is the f-number of the lens and f = focal length of the lens D = diameter of the lens Sayfa 35
Airy Disk Image of two point sources as a function of distance Sayfa 36
Airy Disk As focused Airy patterns from different details on the object come close together, they begin to overlap (refer to our application note Contrast for more information). When the overlapping patterns create enough constructive interference to reduce contrast, they eventually become indistinguishable from each other. Figure shows the difference in spot sizes between a lens set at f/2.8 and a lens set at f/8. As pixels continue to reduce in size, this effect becomes more of an issue and eventually is very difficult to overcome. Sayfa 37
Airy Disk Airy Disk Diameter (μm) f/# at a Wavelength of 520nm --- ----- 1.4 1.78 2 2.54 2.8 3.55 4 5.08 5.6 7.11 8 10.15 11 13.96 16 20.30 Sayfa 38
Grating A large number of equally spaced parallel slits is called a diffraction grating. Gratings containing 1,000 lines per millimeter are common, and are very useful for precise measurements of wavelengths. Sayfa 39
Grating The angle can be measured to very high accuracy, so the wavelength can be determined to high accuracy using the following equation: Sayfa 40
References [1]. R. E. Fischer, Optical System Design, Mc Graw Hill 2nd Ed (2008) [2]. R. Kingslake, Lens Design Fundamentals, Spie Press 2nd Ed (2010) [3]. D. C. O Shea, Elements of Modern Optical Design, John Wiley & Sons Inc (1985) [4]. J.M. Geary, Lens Design, Willmann-Bell, Inc (2002) Sayfa 41