# Wave Interference, question on diagram

I'm trying to understand the wave behavior of light and have questions on diagrams of it. Wiki shows the following two diagrams from Christian Huygens describing the wave nature of light. I have seen similar diagrams elsewhere. How do the black curved lines in these diagrams relate to the third, showing an electro magnetic wave? Are the peaks of $$\vec E$$ in red equivalent to the curved black lines? Also, do the black lines represent peaks on one side of the surface wave in the fourth picture?