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Lil_Aziz1

- 21

- 1

__College Physics__by Serway / Vuille 8th Edition. This is what it says:

"To analyze the diffraction pattern, it's convenient to divide the slit into halves, as in Figure 24.17 (picture below). All the waves that originate at the slit are in phase. Consider waves 1 and 3, which originate at the bottom and center of the slit, respectively. Wave 1 travels farther than wave 3 by an amount equal to the path difference [tex] \frac{a}{2}\sin\theta[/tex], where a is the width of the slit. Similarly, the path difference between waves 3 and 5 is [tex] \frac{a}{2}\sin\theta[/tex]. If this path difference is exactly half of a wavelength, the two waves cancel each other and destructive interference results. Therefore, waves from the upper half of the slit interfere destructively with waves from the lower half of the slit when

[tex] \frac{a}{2}\sin\theta = \frac{\lambda}{2} [/tex]

The question is: why is a/2 the hypotenuse? why not just use a? I realize the first sentence says, "it's convenient to divide the slit into halves," but why?