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(a) Find the equation of a at which intensity extrema for single-slit diffraction occur (Im - is maximum). What are the (b) smallest a and (c) associated m, the (d) second smallest a and (e) associated m, and the (f) third smallest a and (g) associated m? (Note: To find values of a satisfying this conditiion, plot the curve y = tan a and the straight line y = a and then find their intersections, or use a calculator to find an appropriate value of a by trial and error. Next, from a = (m+1/2)x, determine the values of m associated with the maxima in the single-slit pattern. These m values are not integers because secondary maxima do not lle exactly halfway between minima.) (a)

(a) Find the equation of a at which intensity extrema for single-slit diffraction occur (Im - is maximum). What are the (b) smallest a and (c) associated m, the (d) second smallest a and (e) associated m, and the (f) third smallest a and (g) associated m? (Note: To find values of a satisfying this conditiion, plot the curve y = tan a and the straight line y = a and then find their intersections, or use a calculator to find an appropriate value of a by trial and error. Next, from a = (m+1/2)x, determine the values of m associated with the maxima in the single-slit pattern. These m values are not integers because secondary maxima do not lle exactly halfway between minima.) (a)

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**Chapter 36, Problem 017** (a) Find the equation of \(\alpha\) at which intensity extrema for single-slit diffraction occur (\(I_m\) is maximum). What are the (b) smallest \(\alpha\) and (c) associated \(m\), the (d) second smallest \(\alpha\) and (e) associated \(m\), and the (f) third smallest \(\alpha\) and (g) associated \(m\)? *(Note: To find values of \(\alpha\) satisfying this condition, plot the curve \(y = \tan \alpha\) and the straight line \(y = \alpha\) and then find their intersections, or use a calculator to find an appropriate value of \(\alpha\) by trial and error. Next, from \(\alpha = (m + \frac{1}{2}) 2 \pi\), determine the values of \(m\) associated with the maxima in the single-slit pattern. These \(m\) values are not integers because secondary maxima do not lie exactly halfway between minima.)* (a) (b) \( \alpha = \) Number \(\text{ }*1\) Units (c) \( m = \) Number \(\text{ }*2\) Units (d) \( \alpha = \) Number \(\text{ }*3\) Units (e) \( m = \) Number \(\text{ }*4\) Units (f) \( \alpha = \) Number \(\text{ }*5\) Units (g) \( m = \) Number \(\text{ }*6\) Units
Transcribed Image Text:**Chapter 36, Problem 017** (a) Find the equation of \(\alpha\) at which intensity extrema for single-slit diffraction occur (\(I_m\) is maximum). What are the (b) smallest \(\alpha\) and (c) associated \(m\), the (d) second smallest \(\alpha\) and (e) associated \(m\), and the (f) third smallest \(\alpha\) and (g) associated \(m\)? *(Note: To find values of \(\alpha\) satisfying this condition, plot the curve \(y = \tan \alpha\) and the straight line \(y = \alpha\) and then find their intersections, or use a calculator to find an appropriate value of \(\alpha\) by trial and error. Next, from \(\alpha = (m + \frac{1}{2}) 2 \pi\), determine the values of \(m\) associated with the maxima in the single-slit pattern. These \(m\) values are not integers because secondary maxima do not lie exactly halfway between minima.)* (a) (b) \( \alpha = \) Number \(\text{ }*1\) Units (c) \( m = \) Number \(\text{ }*2\) Units (d) \( \alpha = \) Number \(\text{ }*3\) Units (e) \( m = \) Number \(\text{ }*4\) Units (f) \( \alpha = \) Number \(\text{ }*5\) Units (g) \( m = \) Number \(\text{ }*6\) Units
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