Mechanism for Light Echo Proposed

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I may have got something wrong. But I did not miss what Scot Devlin proposed. I seem to have misunderstood it. Here is the test I did; mathematically. I made a clumsy diagram. The ray that went straight up, then down, A, went through 18 small squares. For the other three, B to D, I had to count diagonal lines by the theorem of Pythagoras. Like B, 14 down after hitting the parabola, but how many up? 3.5 sideways and 8 upwards. Square both, add together, take square root, makes 8.7321 (and some more decimals). Add to 14 = 22.7321. C, 12 down, and the diagonal is 6^2 + 5.5^2 and the square root of that is 8.14, add 12 to that, 20.14. And D, 9 down and for the diagonal, 7^2 + 3^2 is 58, the square root of which is 7.616, gives 16.616.

First visible should be A' - non-reflected, not 6 up and 12 down, just 6 down.

Next one would have D, light passing 16.616 squares, then C, light passing 20.14 ones, then B, light passing through 22.732 squares. So, first centre, then outermost, then going in from there.

In fact, this is one point where I seem to have been deluded by a bad diagram, since as Scot Devlin mentions, all paths should have equal length:

Parabolas connect reflection points of ray paths of the same lengths and therefore the same arrival times.

Now, the point is, the reason for different paths going outward is light hitting successively expanding parabolic surfaces. I wasted my time trying to see if the paths would be longer and longer along A to D on a static parabola.

But why would a parabola expand as a parabola, rather than a sphere expanding as a sphere? And how would this not involve the parabola expanding "quicker than light" if the model were true?

While this one might be possible, mine has the advantage of simplicity. The explanation offered by Scot Devlin might have the rhetoric advantage of "too complicated to check" (for most, including for me). A bit like Superman getting superpowers under the yellow sun, because born under a red one.

Hans Georg Lundahl
Paris
St. Jeanne Françoise Frémiot de Chantal
21.VIII.2021

Sanctae Joannae Franciscae Fremiot de Chantal, Ordinis Sanctimonialium Visitationis sanctae Mariae Institutricis, cujus natalis dies Idibus Decembris memoratur.