And what country can preserve its liberties if their rulers are not warned from time to time that their people preserve the spirit of resistance? Let them take arms. The remedy is to set them right as to facts, pardon and pacify them. What signify a few lives lost in a century or two? The tree of liberty must be refreshed from time to time with the blood of patriots and tyrants.
Monday, September 28, 2020
Angle of incidence = Angle of reflection. Strangely Satisfying
Cut that in half horizontally and you have a whisper gallery. There was a government building with a ceiling like that. What ever was whispered at the left point was easily hear at the right. No more staff meetings allowed....
Your satellite dish is partially the same shape. Those points are called the focus. Math is good.... parabolic sections.... oh baby....
Just pulled down a large Hughes dish last week and the "bowl" was not nearly as deep as that. The focal point at the end of the feedhorn was about a foot outside the rim of the dish. I might make a big birdbath out of it, or a sonic ear.
The law of reflection says that for specular reflection the angle at which the wave is incident on the surface equals the angle at which it is reflected.
I think I'm having a calculus flashback. My Calculus II AND III professor in Engineering school had been a mathematician on the Manhattan Project in his younger days and we spent a lot of time with conic sections, hyperbolic and parabolic sections.
If you take the ellipse shown and revolve it around an axis through the 2 foci and then cut off one end of the resulting solid you have a parabolic dish.
As noted above the law of reflection sends all rays back to the foci of the parabola 3 dimensions as well a 2. That's why the little receiver that sticks out of a dish antenna is where it is
Not just all concentrated at the foci, but equidistant from the far source as well i.e. all wave fronts remain in phase, or it doesn't work right. Cool math, nonetheless. Twas the blue math book in HS, IIRC.
What I think is fun is that the 2 segments of each 'ray' (the part from the source to the edge and from the edge to the end point) all sum up to the same value. Every path there is the same length
It's interesting to note that the rays leaving the left focus are almost identical to the rays entering the right. There is, however, the case of a ray leaving the left focus, directly on the axis of the foci. It travels leaftward, rebounds from the left wall, passes thru the left focus, now moving toward the right focus, and stops when it gets there. Thus (always wanted to use that word in a real sentence) the two sets of rays, one leaving the left focus and one entering the right, are not identical.
Cut that in half horizontally and you have a whisper gallery. There was a government building with a ceiling like that. What ever was whispered at the left point was easily hear at the right. No more staff meetings allowed....
ReplyDeleteYour satellite dish is partially the same shape. Those points are called the focus. Math is good.... parabolic sections.... oh baby....
Just pulled down a large Hughes dish last week and the "bowl" was not nearly as deep as that. The focal point at the end of the feedhorn was about a foot outside the rim of the dish. I might make a big birdbath out of it, or a sonic ear.
DeleteNot parabolic. Elliptical.
DeleteHohlraum. The guts of an H-Bomb.
ReplyDeleteThe law of reflection says that for specular reflection the angle at which the wave is incident on the surface equals the angle at which it is reflected.
ReplyDeleteI think I'm having a calculus flashback. My Calculus II AND III professor in Engineering school had been a mathematician on the Manhattan Project in his younger days and we spent a lot of time with conic sections, hyperbolic and parabolic sections.
ReplyDeleteIf you take the ellipse shown and revolve it around an axis through the 2 foci and then cut off one end of the resulting solid you have a parabolic dish.
As noted above the law of reflection sends all rays back to the foci of the parabola 3 dimensions as well a 2. That's why the little receiver that sticks out of a dish antenna is where it is
Not just all concentrated at the foci, but equidistant from the far source as well i.e. all wave fronts remain in phase, or it doesn't work right. Cool math, nonetheless. Twas the blue math book in HS, IIRC.
Delete/DW
What I think is fun is that the 2 segments of each 'ray' (the part from the source to the edge and from the edge to the end point) all sum up to the same value. Every path there is the same length
ReplyDeleteAlso used for 1nm YAG laser cavities, where a Krypton flash tube at one focal point pumps the YAG rod at the other one.
ReplyDeleteI think I'm in the wrong class...
ReplyDeleteIt's interesting to note that the rays leaving the left focus are almost identical to the rays entering the right. There is, however, the case of a ray leaving the left focus, directly on the axis of the foci. It travels leaftward, rebounds from the left wall, passes thru the left focus, now moving toward the right focus, and stops when it gets there. Thus (always wanted to use that word in a real sentence) the two sets of rays, one leaving the left focus and one entering the right, are not identical.
ReplyDelete