Greeting from Palmia Observatory
Well this week we look at the sun for any spots and introduce the atmospheric scattering equation and then finish up with some symmetry and mirror image flipping and leave you with a puzzle to solve.
First up, there are a few small spots on the sun as you can see in this black and white image. The spots are quite small and I really need a little bigger lens, say 600mm, to get more detail. In the meantime, the clouds are showing up again.
|B&W, 300mm solar image with sunspots (left of center) (Source: Palmia Observatory)|
On our recent blog post comparing the estimated sky brightness of something like the Anza observing site and another site that is being evaluated as part of a night stop on an upcoming road trip through Las Vegas. To that end, Gravity Guy and Part-time Las Vegan, Ken, commented about the effects of the elevation difference between some places like Anza and Needles, CA. Yes, the elevation affects the amount of scattering. It turns out that an observing location at elevation of Anza, say about 3900 feet has an air density of only about 60% of that at Needles at about 500 feet. This difference in air density also means that the scattered light from nearby sources will about 60% of the light scattered from the lower elevation.
The scattering discussion provided in the last week blog of March 22 was mostly a first order approximation of sky brightness at a location on a road trip with possible stop over to try to photograph the Zodiacal light. In that blog post we considered the amount of scattered light that originated as light pollution from large cities and did not take into account all the factors that can affect scattering. So for now, let's just introduce one equation that governs the amount of atmospheric light scattering. Here you can see that the amount of scattered light goes up with air density, which means that there are more air molecules from which light can be scattered. The pattern of scattered light is a cosine squared function of the angle of incoming light. The amount of scattered light also varies indirectly with the 4th power of the light wavelength. The observed sky is blue because the blue wavelengths of light from the sun are scattered more than the other wavelengths.
|Rayleigh atmospheric scattering equation (Source: www.alanzucconi.com)|
So that is enough of equations for now. This next and final discussion covers some aspects of symmetry, particularly mirror symmetry. Check out the following screenshot from ASCPhysicsAndAstronomy website, where the instructor is writing on a transparent "blackboard." Don't pay any attention to the equations, we are done with equations for now, unless you really like doing bra-ket type calculations, but just consider how it is that the instructor is able to write out this equations on the blackboard? Is she just really good, not only of physics, but in writing out the formulas backwards so that we can see them?
We have seen this transparent blackboard before in the Coursera General Relativity course from the Russian Higher School of Economics. Well, we know from these previous examples of using a transparent blackboard that one way of accomplishing this is just by flipping the video images, as if in a mirror, so that the writing comes out looking the way we expect it to.
|Doing physics & writing backwards on transparent blackboard? (Source: ASCPhysicsAndAstronomy)|
So, if it all is done just by flipping the image, horizontally, let's conduct this experiment here in the observatory. So in this next photo, Resident Astronomer George is writing on a glass door, which sort of makes a transparent blackboard. Can you tell what has been written?
|Resident Astronomer tries writing on transparent blackboard (Source: Palmia Observatory)|
Well, let's just use some photo processing software, like Photoshop, and flip the image and see what happens. Hmm, yep, now we can make out what the scribbled writing says: "Ruby jumped over the lazy red fox!"
So, the text is understanding and just like in the real instructional video we get to see the instructor facing us as she writes on the board. Note though that in the original image, I am writing with my "right" hand, but in the flipped image, it looks like I am writing with my "left" hand. Yep, that is what happens with mirror images. But, we have demonstrated who these instructional videos can be made. The only thing there can't be any observers in the audience when the video is being recorded because all of the writing will appear backwards.
|The secret to writing "backwards" is flipping the image in software (Source: Palmia Observatory)|
Ok, let's keep going on this symmetry issue and try one more example of photo images and mirror images. Quantum Field Theory uses a lot of symmetry considerations, so let's use the A. Zee textbook as an example of image flipping. Pay attention to the title of the book for changes and remember that I always wear my watch on my left hand.
|Let's do some more image symmetry flipping with textbook (Source: Palmia Observatory)|
This is just an enlarged version of the previous image.
|Close up image of QFT textbook held in right hand (Source: Palmia Observatory)|
Ok, so now, let's flip the image about the horizontal and see what it looks like. Hmm, now the title text is mirror reversed, just like we expected. Also, I now seem to be holding the book in my left hand, but that is not really the case.
|Textbook, still held in right hand, but image has been flipped (Source: Palmia Observatory)|
Ok, so let's try this flipping one more time. This time I have played a little trick on you so pay attention to the images. Hey, what happened to the textbook?
|Now, let's repeat this experiment with a similar textbook (Source: Palmia Observatory)|
In this enlarged image you can see that the book seems to be held in my right hand but the text is reversed.
|Hey, what happened to the QFT textbook title in this image (Source: Palmia Observatory)|
Let's just flip this image so to make it a mirror image and now look at what happened. Now we can read the text correctly.
|Oh-oh, now what happened in this image (Source: Palmia Observatory)|
Did you figure out what the possible trick was? I'll let you in on my version of the trick next time.
Until next time, here from our burrow, stay safe, as we recover more of our freedom,