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(a) Show that the values of a at which intensity maxima for single-slit diffraction occur can be found exactly by differentiating the following equation Io = Im ( sina) with respect to a and equating the result to zero, obtaining the condition tan(a)= a. (remember, a = sin , although you don't need that for this problem) 2 = (b) Find the values of a satisfying this relation by plotting the curve y=tan(a) and the straight line y=α and finding their intersections. (c) Find the (noninteger) values of m corresponding to successive maxima in the single-slit pattern. Note that the secondary maxima do not lie exactly halfway between minima.

(a) Show that the values of a at which intensity maxima for single-slit diffraction occur can be found exactly by differentiating the following equation Io = Im ( sina) with respect to a and equating the result to zero, obtaining the condition tan(a)= a. (remember, a = sin , although you don't need that for this problem) 2 = (b) Find the values of a satisfying this relation by plotting the curve y=tan(a) and the straight line y=α and finding their intersections. (c) Find the (noninteger) values of m corresponding to successive maxima in the single-slit pattern. Note that the secondary maxima do not lie exactly halfway between minima.

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(a) Show that the values of a at which intensity maxima for single-slit diffraction occur can be found exactly by differentiating the following equation Io = Im α with respect to a and equating the result to zero, obtaining the condition tan(a)= a. (remember, a = =4 sin a πα = sin , although you don't need that for this problem) (b) Find the values of a satisfying this relation by plotting the curve y=tan(a) and the straight line y=α and finding their intersections. (c) Find the (noninteger) values of m corresponding to successive maxima in the single-slit pattern. Note that the secondary maxima do not lie exactly halfway between minima.
Transcribed Image Text:(a) Show that the values of a at which intensity maxima for single-slit diffraction occur can be found exactly by differentiating the following equation Io = Im α with respect to a and equating the result to zero, obtaining the condition tan(a)= a. (remember, a = =4 sin a πα = sin , although you don't need that for this problem) (b) Find the values of a satisfying this relation by plotting the curve y=tan(a) and the straight line y=α and finding their intersections. (c) Find the (noninteger) values of m corresponding to successive maxima in the single-slit pattern. Note that the secondary maxima do not lie exactly halfway between minima.
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