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please need help. Have a test this week and need a complete explanation in full

ID: 2299118 • Letter: P

Question

please need help. Have a test this week and need a complete explanation in full detail about this question.

Lei light be incident on a single slit with width D = lambda and a screen for viewing at L D. Show that a ray from the top of the slit and a ray half way down the slit interfere at an angle: sin(theta) = lambda/D At what other angles will the two rays destructively interfere? (Your answer should be a series involving an index, m). Use Huygens principle to explain why all of the light will destructively Interfere at those angles. Is the central maximum wider or narrower for longer wavelengths?

Explanation / Answer

(d)

when the wavelength (?) is much smaller than the aperture width (d), the wave simply travels onward in a straight line, just as it would if it were a particle or no aperture were present. However, when the wavelength exceeds the size of the aperture, we experience diffraction of the light according to the equation:

sin? = ?/d

Where ? is the angle between the incident central propagation direction and the first minimum of the diffraction pattern. The experiment produces a bright central maximum which is flanked on both sides by secondary maxima, with the intensity of each succeeding secondary maximum decreasing as the distance from the center increases