land raider manual

land raider manual

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land raider manualIf you continue browsing the site, you agree to the use of cookies on this website. See our User Agreement and Privacy Policy.If you continue browsing the site, you agree to the use of cookies on this website. See our Privacy Policy and User Agreement for details.You can change your ad preferences anytime. Find Yourself First. Edition by Kasap. Full clear download (no formatting errors) at:Second Edition. Safa Kasap. Revised: 11 December 2012. Check author's website for updatesPlease check the above website. ReportChapter 2 2.2Chapter 2. Note: Printing errors and corrections are indicated in dark red. Currently none reported.E(y, z,t) 2Eo cos(m y 2The planar waveguide is symmetric, which means that the intensity, E2Choose suitable values and plot the relativeSolution. E(y) Eo cos(t m z m z ) Eo cos(t m z m z). E(y, z,t) 2Eo cos(m y ? 1The first cosine term represents the field distribution along y and the second term is the propagation ofThus, the amplitude is. The intensity is maximum or minimum at the center.Chapter 2 2.3. Figure 2Q1-1 Amplitude of the electric field across the planar dielectric waveguide.Allowed upward and downward traveling waves inside the core of the planarPut differently, a wave startingFigure 2.51 Upward and downward traveling waves along y set-up a standing wave. The condition for setting-up aSolution. From Figure 2.51 it can be seen that the optical path is. AB BA 4a. With the ray under going a phase change with each reflection the total phase change isChapter 2 2.4. The wave will replicate itself, is the phase is same after the one round-trip, thusHence find the amplitude of the field variation along y, across the guide. What is your conclusion? Figure 2.52 Rays 1 and 2 are initially in phase as they belong to the same wavefront. Ray 1 experiences total internalSolutionThe phase difference between the waves meeting at C isChapter 2 2.5Then, m 2k1(a y)cosm m 2k1(a y)Thus, the amplitude Eo is. E 2AcosSee Figure 2Q1-1.http://cobansazgrubu.com/userfiles/horizon-e900-elliptical-manual.xml

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Plot the fieldChapter 2 2.6Ray 1 experiences total internalSolution. The two waves interfering at C are out phase by,E 2AcosThus, the amplitude Eo is. E 2AcosExample 2.1.1 in the textbook, the waveguide condition isChapter 2 2.7The above two equations can be solved graphically as in Example 2.1.1 to find m for each choice of m. Alternatively one can use a computer program for finding the roots of a function. The above equationsThere is no significant difference between the TE and TM modes (the reason is that n1 and n2 are veryFigure 2Q4-1 Field distribution across the core of a planar dielectric waveguide. E 2cosThis is shown in Figure 2Q4-1.Chapter 2 2.8Solution. The waveguide condition isThe above two equations can be solved graphically as in Example 2.1.1 to find m for each choice of m. Alternatively one can use a computer program for finding the roots of a function. The above equationsChapter 2 2.9Suppose that is the delay time between the TE and TM waves over a length L. Then,It is assumed that the math-software package can carryBoth and are now a function of in Eqs (1) and (2). Then the group velocity is found byChapter 2 2.10. Solution. The results shown in Figure 2.11, and Figure 2Q6-1 were generated by the author using LiveMath basedThe important conclusionThus, it is only approximate. Figure 2Q6-1 Group velocity vs.The refractive index of GaAs is 3.66 and that of the. AlGaAs layers is 3.40. What is the cut-off wavelength beyond which only a single mode can propagateChapter 2 2.11What is the mode field widthSolutionChapter 2 2.12Propagation constants () at other wavelengths and hence frequencies () can be similarly calculated. The results are listed in Table 2Q8-1 and plotted in Figure 2Q8-1. This is the dispersion diagram. ForThey are drawn so that the. Thus, the solutions of the waveguide condition as in Example 2.1.1 generates the data in Table 2Q8-1Chapter 2 2.http://www.g-flow.com/images/editor/how-does-automated-manual-transmission-works.xml13Author's Note: Remember that the slope at a particular frequency is the group velocity at thatCompare your MFW calculation. SolutionChapter 2 2.14Solve the waveguide conditionThen useWe can also calculate MFW fromAuthor's Note: Consider a more extreme caseChapter 2 2.15Calculate the maximum acceptance angle. (e) Calculate the modal dispersion and hence the bit rateSolutionNumber of modes M,The numerical aperture NA is. If max is the maximum acceptance angle, then,Modal dispersion is given byL c 3108Given that 0.29, maximum bit-rate isWe neglected material dispersion at this wavelength which would further decrease BL. MaterialChapter 2 2.16. For example, assuming an LED with a spectral rms deviation of about 20 nm, and a Dm 200 ps km-1The refractive index of water is 1.330. Consider a water jet of diameter 3 mm that is illuminated by green light of wavelength 560 nm. What isHow many modes are there? WhatThe diameter of the jet increases (slowly) as the jet flows away from theLight guided along a thin water jet. A small hole is made in a plastic soda drinkWhen the hole is illuminated with aWater with air bubbles (produced by shakingAir bubbles scatter light andFirst such demonstration has been attributed to Jean-. Daniel Colladon, a Swiss scientist, who demonstrated a water jet guiding light inV-numberNumerical apertureThe large difference in refractive indices between the water and the air ensures that total internalChapter 2 2.17Is this a single mode fiber? (b) Calculate the wavelength below which theSolutionChapter 2 2.18Is this a single mode fiber? (b) Calculate theCalculate the maximum total acceptance angle. (e) Calculate the material, waveguide and chromaticSolutionV-number is given byChapter 2 2.19The first equation can beSolutionTaylor expansion around x 0 and truncating the expression, keeping only the linear term yields,Chapter 2 2.20Change the operating wavelength to by a small amount, sayThen determine the group velocity vg ofHow do your resultsSolution.https://labroclub.ru/blog/electrolux-ebm4300sc-manual From example 2.3.4, we haveGroup VelocityComparing to Example 2.3.4Chapter 2 2.21Solution. The Sellmeier equation isSellmeier A1 A2 A3 1SiO2 (fused silica) 0.696749 0.408218 0.890815 0.0690660 0.115662 9.900559Apply NA n2The refractive index n(x) of SiO2-x mol.GeO2, assuming a linear relationship, can be written asSince Ng will depend on the wavelength, show that the material dispersion coefficient Dm is givenDmLd? c d2. Using the Sellmeier equation and the constants in Table 1.2 in Ch. 1, evaluate the material dispersion. Solution. From Ch. 1 we know thatChapter 2 2.22Differentiate with respect to wavelength using the above relationship between Ng and n. L LNg1Thus, Dm. Ld?The 1, 2, 3 are in m.Figure 2Q17-1 Materials dispersion Dm vs.Matlab can also be used.)Chapter 2 2.23It is present even when theLet us suppose that n1 and n2 are wavelength (or k)The group velocity is defined and given byShow that the propagation time, or the group delay time, of the mode is. L Ln2 Ln2 d(kb)Given the definition of V,Show thatV (6)w. Ld? c dV 2Chapter 2 2.24Waveguide dispersion coefficient (9)Suppose that a 1.3 m laser diode with a spectralEstimate the waveguide dispersion perFigure 2.53 d2Electronics Engineer, 51, 313, 1981.). Solution. Waveguide dispersion arises as a result of the dependence of the propagation constant on the V-numberIt is present even when the refractive index is constant; no materialSuppose that is the. Then the normalizedThe group velocity is defined and given byThus, the propagation time of the mode isChapter 2 2.25Given the definition of V,From Eq. (5),This means that depends on V as. Ln2 Ln2 d(Vb)Dispersion, that is, spread in due to a spread can be found by differentiating Eq. (6) to obtain,The waveguide dispersion coefficient is defined asV (8)w. Ld? c dV 2. In the range 2 Chapter 2 2.26Consider a fiber with a core of diameter of 8 m and refractive index of 1.468 and a claddingSuppose that a1.3 m laser diode with aEstimate the waveguide dispersionFrom the graph, Vd2Dw 4.610-6Using Eq. (10). Dw ?Dw 4.610-6However, there is an additional dispersion mechanismConsider a light source with a range of wavelengthsWe can view this as a change in the input wavelength. Suppose that n1, nThe propagation time, or the group delay time, g per unit length is. Since depends on n1, and V,Chapter 2 2.27The mathematics turns out to be complicated but the statement in Eq. (2) is equivalent toEven the statement in Eq.The total intramodeSolution. Total dispersion in a single mode step index fiber is primarily due to material dispersion and waveguideSuppose that n1, n 2, hence depends on the wavelength. The propagation time, or the group delay time, g per unit length isSince depends on n1, and V, let us consider g as a function of n1, (thus n2) and V. A change?Using the partial differential chain rule,Chapter 2 2.28The mathematics turns out to be complicated but the statement in Eq. (2) is equivalent toEven the above statement in Eq.The total intramodeVb d. D ?g1Waveguide dispersion. Dw ?Dw 5.6 ps km-1Profile dispersion is more than 10 times smaller than waveguide dispersion.Chapter 2 2.29Consider theSolution. Consider the Taylor expansion for, a function of wavelength, about its center around, say at 0, when weThen, Taylor's expansion gives,L 2 1 km ? -2 -1 2What would be theSolution. DispersionBit rateOptical bandwidthChapter 2 2.30What should be the linewidth of the laser source so that over 100 km,SolutionThe rms dispersion isAssume that the input light spectral width is 1 nm. SolutionSolution. For the single mode fiber, the small core diameter is to ensure that the V-number is below the cutoffChapter 2 2.31For multimode fibers, the larger core size allows multiple modes to propagate in the fiber and thereforeFurther, the larger diameter results in a greater acceptance angle. Thus. LEDs, which are cheaper and easier to use than lasers, are highly suitable. The total diameter of the coreWhat is its NA at the fiber axis, and its effective NA? SupposeThe material dispersion coefficient at this wavelength is about 5 ps km-1How does this compare with theWhat would the total dispersion. Solution. Modal dispersion for 1 km of graded index fiber is. Ln1 2 (1000)(1.474) 2Assuming a Gaussian output light pulse shape, rms material dispersion is. Total dispersion isL c. Maximum bit-rate isChapter 2 2.32The corresponding B for 1 km would be around 13 Mb s-1. With LED excitation, again assuming a Gaussian output light pulse shape, rms material dispersion isTotal dispersion isCalculate, the total dispersion and estimate the bit-rate distance product of theSolution. Modal dispersion for 1 km of graded index fiber is. Ln1 2 (1000)(1.474) 2Assuming a Gaussian output light pulse shaper. Total dispersion isL c 3108Chapter 2 2.33Maximum bit-rate would beThe corresponding B for 1 km would be around 13 Mb s-1Assume that a laser is to be used with this fiber and the laser. What type of dispersion do you thinkSolutionWe can now calculate intermodal dispersionThe total dispersion for 850 nm isSo the intramodal dispersion isChapter 2 2.34If is the profile index then the rms intermodal dispersion is given by2. LnThe optimum profileSolutionChapter 2 2.35. From the graph in Figure 2Q28-1From the graph in Figure 2Q28-1, a 3.4 changeFigure 2Q28?1What are O and O? (b) How wouldWhat is O? (c) Sketch ray paths forWhere is O? (d). What use is 0.23P GRIN rod lens in Figure 2.32(c)? Figure 2.32 Graded index (GRIN) rod lenses of different pitches. (a) Point O is on the rod face center and the lens focusesSolutionChapter 2 2.36O and O are the focal points of the lenses (approximately). (Schematic only). (b) TheFigure 2Q29-2: Ray paths in a GRIN rod that has a pitch between 0.25P to 0.5P. (Schematic only.)Possible AnswersReduce scattering by reducing density and hence refractive index nUse a glass material with a lower glass transition temperatureAssume that all the light was launched into the fiber. The fiber is quoted asChapter 2 2.37Solution. Pout Pin exp(L)The first part of the experiment involvesThe output power Pnear is measured at the near end from the short cut fiber. The attenuation is then givenUsually a mode scrambler (mode stripper) is used forThe power output from a particular fiber is measured to be 13 nW. Then, 10 km of fiber is cut-out and the power output is measured again and found to be 43 nW. What isFigure 2.54 Illustration of the cut-back method for measuring the fiber attenuation. S is an optical source and D is aChapter 2 2.38Actual values would be less. SolutionWhen the wavelength is 1490 nmAR 0.918dB km ?mAt 850 nm and 1300 nm the FIR. At 850 nm,Chapter 2 2.39T B fAR 1.111dB km ?mAt 1300 nm,AR 1.111dB km ?mRayleigh scattering process decreases with wavelength, and as mentioned in Ch. 1, it is inverselyRayleigh scattering is approximately given by two sets of different equations in the literature3Fiber is drawn at high temperatures and asHowever, note that the reportedChapter 2 2.40It is found that for a single mode fiber withSolution. We expect the bending loss vs. R on a semilogarithmic plot to be as in Figure 2Q35-1 (schematic). Figure 2Q35-1 Microbending loss decreases sharply with the bend radius R. (Schematic only.). Expected R with V (1). Expected R with (3)? Eqs. (3) and (4) correspond to the general statement that microbending loss gets worse whenObservation R with (5). Consider the penetration depth into a second medium (Example 2.1.3),Chapter 2 2.41Thus, increases with decreasing. Thus, from Eqs. (3) and (6), we expect. Expected R with with (7) Thus Eq, (7)Thus, takingR constant (9). We are interested in the R behavior at a constant. We can lump the constant into ln and obtain,Figure 2Q35-2 The relationship between and the radius of curvature R for a given amount of bending loss.Chapter 2 2.42The trench fibers have a trench placed in the cladding where the refractivePlot the bending lossSuppose that we set our maximum acceptable bending loss toData over 1.55 - 1.65 m range. (Note, data used from a number of sources: (a). M.-J. Li et al. J. Light Wave Technol., 27, 376, 2009; (b) K. Himeno et al, J. Light Wave Technol., 23, 3494, 2005; (c) L.- A. Standard SMFTrench Fiber 1bTrench Fiber 2cNanoengineered FiberaChapter 2 2.43Trench 1. Trench 2. Nanoengineered. Expon. (Standard SMF). Expon. (Trench 1). Expon. (Trench 2). Expon. (Nanoengineered)Figure 2Q36-1 Attenuation per turn as a function of bend radius. Standard SMF, 13 mm; trench 1, 10 mm; trench 2, 6 mm; nanoengineered, 3 mm.We will calculate approximately given various fiber parameters using the single mode fiberWhat is your conclusion? (You might wish to compareChapter 2 2.44Chapter 2 2.45Figure 2Q37-1 Bending loss B vs.Results compare reasonably with the experiments in Figure 2.56 given the approximate nature of theWhat should beIf the amplitude of the index variation n is 2?10-5FBG is 5 mm, what are the maximum reflectance at the Bragg wavelength and the bandwidth of the. FBG? Assume that the effective refractive index n is 1.460. What are the reflectance and the bandwidthChapter 2 2.46R tanh2The parameterTwo neighboring sensors haveWhat would beWhat is the strain at fracture if the fiber fractures roughly at anWhat is your conclusion? SolutionThe shift due to strain is (only B is strained). Maximum strain occurs whenChapter 2 2.47The separation between the Bragg. Shift due to strain is now. Which must be B2 B1 so thatThe main problem is precise compensation of temperature. Solutions Manual for Optoelectronics and Photonics Principles and Practices 2nd. Edition by Kasap. Full clear download (no formatting errors) at:Now customize the name of a clipboard to store your clips. Connect with us to Instant Access ISBNs are for individuals purchasing with credit cards or PayPal. Savvas Learning Company is a trademark of Savvas Learning Company LLC. Please try again. Mark S. Merkow Jim BreithauptAccounting standards are known as Singapore Financial Reporting Standards (SFRS) an An Please check the above website. All rights reserved. This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. All rights reserved. This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458. Solutions Manual (Preliminary) Chapter 1 1.2 11 December 2012 Preliminary Solutions to Problems and Questions Chapter 1 Note: Printing errors and corrections are indicated in dark red. What is its velocity. All rights reserved. This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458. All rights reserved. This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458. From the imaginary part k 2 ? ? 2 ? o? o? r ? ? 2 Consider the small.Then k 2 ? ? 2 ? o ? o? r and the velocity is ? 1 v? ? k ? o? o? r 1.3 Point light source What is the irradiance measured at a distance of 1 m and 2 m from a 1 W light point source. All rights reserved. This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458. Sometimes, one of the reflectors is a plane mirror. The two spherical mirrors and the space between them form an optical resonator because only certain light waves with certain frequencies can exist in this optical cavity. The radiation inside a spherical mirror cavity is a Gaussian beam. The actual or particular Gaussian beam that fits into the cavity is that beam whose wavefronts at the mirrors match the curvature of the mirrors. Consider the symmetric resonator shown in Figure 1.54 in which the mirrors have the same radius of curvature R. When a wave starts at A, its wavefront is the same as the curvature of A. In the middle of the cavity it has the minimum width and at B the wave again has the same curvature as B. Such a wave in the cavity can replicate itself (and hence exist in the cavity) as it travels between the mirrors provided that it has right beam characteristics, that is the right curvature at the mirrors. The optical cavity contains a Gaussian beam. All rights reserved. This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458. What is your conclusion. All rights reserved. This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458. Which is larger, and why.All rights reserved. This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458. All rights reserved. This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458. Solutions Manual (Preliminary) Chapter 1 1.9 11 December 2012 Figure 1Q8-1 Refractive index n and the group index Ng of pure SiO2 (silica) glass as a function of wavelength (Excel). The minimum in Ng is around 1.3 ?m. Note that the smooth line option used in Excel to pass a continuous smooth line through the data points. All rights reserved. This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458. Solutions Manual (Preliminary) Chapter 1 1.10 11 December 2012 Figure 1Q8-2 Refractive index n and the group index Ng of 86.5SiO213.5GeO as a function of wavelength (Excel). The minimum in Ng is around 1.4 ?m. Note that the smooth line option used in Excel to pass a continuous smooth line through the data points. Data points are exactly on the line and are not shown for clarity. Material dispersion is proportional to derivative of group velocity over wavelength. The corresponding values are close to 1.3 and 1.4 ?m. 1.9 The Cauchy dispersion relation for zinc selenide ZnSe is a II-VI semiconductor and a very useful optical material used in various applications such as optical windows (especially high power laser windows), lenses, prisms etc. All rights reserved. This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458. Calculate the phase velocity and group velocity of light in this medium. All rights reserved. This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458. How do these compare with part (c) and what is your conclusion. All rights reserved. This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458. Solutions Manual (Preliminary) Chapter 1 1.13 11 December 2012. The critical angle is sin. All rights reserved. This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458. The angle of incidence is 40. All rights reserved. This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458. Solutions Manual (Preliminary) Chapter 1 1.15 11 December 2012 1.12 Snell's law and lateral beam displacement An engineer wants to design a refractometer (an instrument for measuring the refractive index) using the lateral displacement of light through a glass plate. His initial experiments involve using a plate of thickness L, and measuring the displacement of a laser beam when the angle of incidence ?i is changed, for example, by rotating (tilting) the sample. All rights reserved. This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458. All rights reserved. This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458. All rights reserved. This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458. Solutions Manual (Preliminary) Chapter 1 1.18 11 December 2012 n ????Deflection angle)? ?L between colors ?L between blue and rede 1.4634 0.5954 rad 34.115? 1.4587 0.5883 rad 33.709? 7.08 mm 1.4567 5853 rad 33.537? 3.00 mm 10.1 mm 1.14 Fermat's principle of least time Fermat's principle of least time in simple terms states that when light travels from one point to another it takes a path that has the shortest time. In going from a point A in some medium with a refractive index n1 to a point B in a neighboring medium with refractive index n2 as in Figure 1.56 the light path is AOB that involves refraction at O and satisfies Snell's law. The time it takes to travel from A to B is minimum only for the path AOB such that the incidence and refraction angles ?i and ?t satisfy Snell's law. Let's draw a straight line from A to B cutting the x-axes at O?. The line AO?B will be our reference line and we will place the origin of x and y coordinates at O?. Without invoking Snell's law, we will vary point O along the x-axis (hence OO.All rights reserved. This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458. Given a choice of two possible antireflection coatings, SiO2 with a refractive index of 1.