(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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8334bf9f-036f-42c6-8278-821b6fa1dd3e%2F8ccfc2d3-4b20-4e3c-a993-321e71970f55%2Ftx3lzd_processed.png&w=3840&q=75)
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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