1087_Physics ProblemsTechnical Physics

1087_Physics ProblemsTechnical Physics - 428*P38.67...

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428 Diffraction Patterns and Polarization * P38.67 (a) Constructive interference of light of wavelength λ on the screen is described by dm sin θλ = where tan θ = y L so sin = + y Ly 22 . Then dyL y m af ej 12 += . Differentiating with respect to y gives dL y dy L y y m d dy d m d dy dL d dy mL y 1 1 2 02 32 2 222 2 ++ F H G I K J = + + == +− + = + −− bg a f a f a f a f (b) Here sin = gives 10 8000 1550 10 2 9 m m sin , = × × F H G I K J sin . . 1 6 6 055 10 10 26 1 m 1.25 m yL ° = tan . tan . . 240 261 118 m m Now d dy dL y = + = × + = 2 6 2 7 125 10 124 1 1 8 377 10 377 a f . .. m 2.40 m m nm cm . P38.68 For a diffraction grating, the locations of the principal maxima for wavelength are given by sin =≈ m d y L . The grating spacing may be expressed as d a N = where a is the width of the grating and N is the number of slits. Thus, the screen locations of the maxima become y NLm a = . If two nearly equal wavelengths are present, the difference in the screen locations of corresponding
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