The figure shows four slits in a diffraction grating. A set of Huygens wavelets

Question

The figure shows four slits in a diffraction grating. A set of Huygens wavelets is spreading out from each slit. Four wave paths, numbered 1 to 4, are shown leaving the slits at angle 1. The dashed lines are drawn perpendicular to the paths of the waves. The shading shows the extra distance traveled by wave 1 that is not traveled by wave 2. I just need d&e

a. How many extra wavelengths does wave 1 travel compared to wave 2? ____ONE_____

b.How many extra wavelengths does wave 2 travel compared to wave 3? __ONE_________

c. As these four waves combine at some large distance from the grating, will they interfere constructively, destructively, or in between? Explain.

constructively

d. Suppose the wavelength of light is doubled (imagine erasing every other wave front in the picture). Would the interference at angle 1 then be constructive, destructive, or in between? Explain. Your explanation should be based on the figure, not an equation.

e. Suppose the slit spacing is doubled (imagine closing every other slit in the picture). Would the interference at angle 1 then be constructive, destructive, or in between? Explain. Again, base your explanation on the figure, not an equation.

Explanation / Answer

d) The path length differences would then corresponds to one-half wavelength so the interference will be destructive.

e) If the slit spacing were doubled,then the path length difference at would increase to two wavelengths and the interference would be constructive.

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