[QUOTE=Uncwilly;219158]When I took math for laser optics years ago I could have done this one.[/QUOTE]
[QUOTE=davieddy;219214][URL]http://www.youtube.com/watch?v=z_4Jf18XDoo&feature=fvst[/URL][/QUOTE]How does that relate to my post?

I actually took such a class, it fulfilled a requirement and got me into the laser optics building/program. I didn't go further as other subject matters were of greater interest.

[quote=Uncwilly;219300]How does that relate to my post?

I actually took such a class, it fulfilled a requirement and got me into the laser optics building/program. I didn't go further as other subject matters were of greater interest.[/quote]

When I first taught at St Paul's (1974) they had just purchased a laser
which made demonstrating optics (eg a diffraction grating) a piece
of cake.
The first time I wheeled it out, that classic Queen record was No 1
and as you know by now, I couldn't resist reciting that lyric.
(See my post title)

David

More to the point, how does your post relate to this thread?

[QUOTE=davieddy;219298]I know ccorn is chomping at the bit, [...][/QUOTE]
Sorry. Of course a solid glass ball makes more sense. However, in fora like these I interpret "sphere" as "spherical shell", and then I try to make sense of the rest.

[QUOTE=davieddy;219298]Refer to ccorn's diagram. Not sure why he has designated the angles by delta, since they aren't small.[/QUOTE]
I wanted to use common names for the angles and looked up Wikipedia entries in several languages. [strike]All of them[/strike]The one I first looked up used [tex]\delta[/tex], so I picked that. Otherwise I would have chosen John Doe names like [tex]\alpha[/tex].

[QUOTE=davieddy;219298]I shall now consider ccorn's last post![/QUOTE]
As long as I haven't made a drawing for this, consider the second intersection point of the ray S'C with the circle, and draw rays to/from that. There are a lot of equal angles in the figure.

Chomping at the bit
 

This is a horse racing metaphor, and was referring to
your eagerness to put the gravity problem to rest.
Welcome aboard!

I'll apply the French Lawnmower (Coup de Grace) to this thread,
and you do the gravity one.

My yardstick for pedagogical skills is Feynman.
But instead of mucking about discovering QED, I spent a lot of
time on justifying a lot of Skool Fizzix that I previously taken for granted.

Instead of Bongos, I was forced(not really) to learn the violin to a
standard better than "horsehair on catgut".

When it comes to being distracted by the fairer sex, I think we
may as well call it quits.

Couple of personal questions:
Age? Location? and "Haven't you been a member here before?"
Your user name sounds familiar, as is your avatar.

As for your (and my) disappointment about the lack of response
to the gravity thread, I post on a pretty varied set of topics.
in varied states of sobriety, thereby ensuring my inclusion on
(nearly) everyone's ignore list.

David

PS I saw a delightful documentary on Feynman in
which he ascribed his powers of inquisition to his father.
Ditto.

[QUOTE=davieddy;219441]This is a horse racing metaphor, and was referring to your eagerness to put the gravity problem to rest.[/QUOTE]
I see. The scientific literature and data books I have swallowed do not contain many real-life proverbs; therefore I am susceptible to such misunderstandings.

[QUOTE=davieddy;219441]I'll apply the French Lawnmower (Coup de Grace) to this thread, and you do the gravity one.[/QUOTE]
[url=http://mersenneforum.org/showthread.php?p=219660#post219660]Done.[/url]

[QUOTE=davieddy;219441]My yardstick for pedagogical skills is Feynman. But instead of mucking about discovering QED, I spent a lot of time on justifying a lot of Skool Fizzix that I previously taken for granted.[/QUOTE]
I like to demonstrate mathematical gems that are at least hundreds of years old and yet haven't been tought to me when I studied the physical engineering sciences. A lot of beautiful things seem to have been hidden from me! As an example, I once decided that I, laden with all my knowledge from university, should be able to find out an algebraic expression for sine and cosine of one-third of an angle (without resorting to complex cube roots, logarithms, arcsines and such). It took me two full weeks to gain the insight that there is no such thing as sought by me, and the ancient Greeks seem to have known that (though the first proof seems to be from the age of Gauss). Well, I am irritated about the fact that such things have missed me. On the other hand, one encounters other interesting gems (strophoides etc) in the course of such quests.

[QUOTE=davieddy;219441]Couple of personal questions:
Age? Location? and "Haven't you been a member here before?"
Your user name sounds familiar, as is your avatar.[/QUOTE]
42, Germany, no. There seem to be further ccorns represented in the internet. Among the Google hits, I am the one who mostly files software bug reports.
There is an abandoned website by me. No point in linking to it. I should take up blogging again.

Use in microscopy
 

In practice, the first element of the objective lens is the flat
surface of a hemisherical glass ball, with the specimen
at the bottom of a layer of oil with the same refractive
index as the glass, thickness R/mu.

The resolution is governed by the angle of the
cone of rays from the the specimen entering the objective,
and the wavelength in oil.
This lens gains on both counts over a dry lens.

David

[quote=ccorn;219281]And the other half appears as if having emerged from the same outside point, but reflected by the glass [strike]sphere[/strike]ball.[/quote]

[quote=ccorn;219357]
As long as I haven't made a drawing for this, consider the second intersection point of the ray S'C with the circle, and draw rays to/from that. There are a lot of equal angles in the figure.[/quote]

Yes indeed: mind boggling!

But even without that beautiful extra construction, note
that the sine rule always applies:

sin OCS'/sin CS'O = Rmu/R = mu

However, when OCS'(=OSC) > 90 it no longer represents
the angle in air r, but (180 - r).
The result follows.

David