A single slit with a width of 0.100 mm is illuminated by light by a wavelength 610 nm.
a) What is the angular location of the first diffraction minimum?
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b) What is the angular location of the second diffraction minimum?
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c) Diffraction maxima occur approximately halfway among adjacent diffraction minima. Using your results from (a) and (b), Compute the approximate angular location of the first diffraction peak to the left or right of the central diffraction peak.
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d) To obtain the "exact" locations of diffraction maxima, values of alpha are needed at which intensity maxima occur for a single slit. An equation for these values of alpha are obtained by differentiating Eq. 36-5 with respect to alpha and equating the result to zero. Two equations are obtained: (1) The first equation, sin / = 0, is the condition that should be satisfied when there is a diffraction minima. (2) The second equation of the form (sin ) n1(cos )n2 = ()n3 is the condition that must be satisfied when there is a diffraction maxima. What are the values of the integer’s n1, n2and n3, at least one of which is negative?
n1= ?
n2= ?
n3= ?
e) It is not possible to precisely solve the equation for diffraction maxima to obtain a general formula for the location of all diffraction maxima; but, the values of alpha that satisfy this equation can be found graphically by plotting the curve y =(sin )n1 (cos )n2 and the curve y = ()n3 and determining where the two curves intersect. The smallest two values of alpha that satisfy the equation are alpha = 0 and alpha = 4.4934. The first solution is exact, and the second and all others are only approximate. Using the solution alpha = 4.4934, solve for the angular location theta of the diffraction peak adjacent to the central peak.
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f) Compute the percent error among the actual value of theta calculated in (e) and the approximate value calculated in (c).%