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Chapter36

# Chapter36 - 1(a The condition for a minimum in a...

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1. (a) The condition for a minimum in a single-slit diffraction pattern is given by a sin θ = m λ , where a is the slit width, λ is the wavelength, and m is an integer. For λ = λ a and m = 1, the angle θ is the same as for λ = λ b and m = 2. Thus, λ a = 2 λ b = 2(350 nm) = 700 nm. (b) Let m a be the integer associated with a minimum in the pattern produced by light with wavelength λ a , and let m b be the integer associated with a minimum in the pattern produced by light with wavelength λ b . A minimum in one pattern coincides with a minimum in the other if they occur at the same angle. This means m a λ a = m b λ b . Since λ a = 2 λ b , the minima coincide if 2 m a = m b . Consequently, every other minimum of the λ b pattern coincides with a minimum of the λ a pattern. With m a = 2, we have m b = 4. (c) With m a = 3, we have m b = 6.

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