Cavemen studied refraction

[Ben the Ignorant]

Not with math but in a practical way.

 

[John]

The Archer Fish worked it out before we did ....:

 

[JRWASTRO]

There was a caveman named Snell

He was really the spear fisherman from hell

He could tell by the bend of the spears end

It was sine theta over sine theta well, well !

 

My best attempt at doggerel,

Jeremy.

[SIDO]

More evidence 😉

[Ouroboros]

1 hour ago, JRWASTRO said:

There was a caveman named Snell

He was really the spear fisherman from hell

He could tell by the bend of the spears end

It was sine theta over sine theta well, well !

 

My best attempt at doggerel,

Jeremy.

They knew the Greek alphabet even before the Greeks did. Amazing. 😉 

Shouldn't that be sine theta over sine phi - angle of incidence and angle of refraction? Just saying! 🙂  

[JRWASTRO]

RE: ... Shouldn't that be sine theta over sine phi - angle of incidence and angle of refraction?

I think theta has a nice ring to it. Poetic licence allowed us to remove the subscripts!!

Naming angles?  Take your pick.

The two angles may be (theta1 and theta2) or (theta_i and theta_r) or (phi1 and phi2)

For me Theta and phi have always been associated with angles eg. polar co-ordinates ... (r,theta, phi).

A sine wave: sin(omega * t +phi) , we could write theta = (omega * t + phi) .

How's That ?

Jeremy.

[Demonperformer]

On 15/05/2019 at 12:57, JRWASTRO said:

RE: ... Shouldn't that be sine theta over sine phi - angle of incidence and angle of refraction?

I think theta has a nice ring to it. Poetic licence allowed us to remove the subscripts!!

Naming angles?  Take your pick.

The two angles may be (theta1 and theta2) or (theta_i and theta_r) or (phi1 and phi2)

For me Theta and phi have always been associated with angles eg. polar co-ordinates ... (r,theta, phi).

A sine wave: sin(omega * t +phi) , we could write theta = (omega * t + phi) .

How's That ?

Jeremy.

But it doesn't rhyme.

[JRWASTRO]

Re:

" But it doesn't rhyme.  "

OK. But  you've got to admit my attempt is not too bad.

Alright I've taken the bait. What are those formulae, in your signature, all about?

Jeremy.

[Demonperformer]

9 hours ago, JRWASTRO said:

What are those formulae, in your signature, all about?

t is the optimal sub-length for a particular telescope, camera and SQM combination ... all condensed from this article. That said, there are some on here who disagree with the specifics. For a bit of discussion, see this thread.

[Ben the Ignorant]

Thought a little more about it and they also knew about opacity and transparency; when the water is too muddy there's no point in hunting there. Also reflection, the Sun reflecting off water hides the prey so they had to chose a spot at a good angle relative to the Sun. Naturally they noticed how light scatter happens because it is another hindrance to that kind of fishing, the more troubled the water the more Sun glitters you take in your eyes, that's painful and it protects the fish.

Same for turbulence inside of water, the more agitated, the less you can aim. Spontaneously, without really thinking about it, one tries to take advantage of tree shadows and such to avoid reflections, so they had a grasp of albedo. And naturally they noticed a low Sun casts reflections at the same low angle, so the equality between incidence angle and reflection angle was understood, even if not formally.

There's not a long path from these observations to the idea of a line perpendicular to the plane of water and starting at the point of reflection, with angles identical on both sides. Straight lines, flat planes, points, angles, symmetry, that is the basic of geometry and it probably started there as much as in other mundane places and activities. Total transparency or total opacity of the water, plus all the in-between cases might have spurred the idea of rates, which is also a mathematical concept.

From just seeing things to noticing them to parsing and studying them, that's how science began.

[JRWASTRO]

Re:

is the optimal sub-length for a particular telescope, camera and SQM combination ... all condensed from this article. That said, there are some on here who disagree with the specifics. For a bit of discussion, see this thread.

 

Wonderful.  I will read "this article"  slowly and in detail. Why?  Because

Quote:
σe=newhere ne is the number of electrons collected by the pixel and σe is the standard deviation of the number of electrons expected between pixels all exposed to the same light intensity.

End quote.

Here he alludes to Poisson distribution.

This article deserves reading.

Thanks.

Jeremy

 

Addition:

Just read the article and it is excellent. Beautifully explained. I have taken note!

JRW

 

[Marvin Jenkins]

They could have just worn polarising shades like me.