ch36-p107 - 107. (a) The central diffraction envelope spans...

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107. (a) The central diffraction envelope spans the range – θ 1 < < + 1 where 1 1 sin , a λ = which could be further simplified if the small-angle approximation were justified (which it is not , since a is so small). The maxima in the double-slit pattern are at m m d = sin , 1 λ so that our range specification becomes 11 1 sin sin sin , m ad a λλ −− ⎛⎞ ⎛ ⎞ −< < + ⎜⎟ ⎜ ⎟ ⎝⎠ ⎝ ⎠ which we change (since sine is a monotonically increasing function in the fourth and first quadrants, where all these angles lie) to
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