After doing these calculations a few times, I noticed that for a 60 degree equilateral prism, the two angles inside the prism (theta 2 and theta 3) add up to 60. Nice little shortcut for equilateral prisms--less geometry!
just about to take my aqa A level physics exam tomorrow and came across your workthroughs for difficult refraction and TIR problems, just what i needed! been stuggling on more complex ones like these for a while and you have helped me alot with this topic! a big thanks to your physics and mathematics playlists, cant wait to see more vids in the future!
This is challenging! I rewatched twice to fully understand. What is difficult in my opinion is knowing to replicate the horizontal beneath the refracted light once more and knowing it is also 30 degrees because it was the angle between the medium and horizontal coming in on the left side, then adding the 5.7 degrees to that because of the reflected angle.
cool fact:If you transpose the light beam such that the normal entry line intersects with one corner of the prism, you can apply angle sum of triangle twice to find the 35.7 deg
thank you very much sir for the video I understand after seeing this video but I have a question 1,56where did you get it from? Thank you in advance sir 🙏🏻
Depends on which "n sin(theta)" you are referring to. If you are referring to the exiting ray, then you'll have internal reflection. (see the videos on total internal reflection)
What should I do if theta 3 is about 40° or bigger? with that IOR, 1.56 * sin(40°) = 1.002... => arcsin from something > 1 isn't possible. Is there a different approach?
Im sure you figured this out by now but I had the same issue. For anyone new: the line perpendicular to the surface has one 90 degree angle. then if you draw a line perpendicular to the bottom of the triangle you can use a combination of complimentary and supplementary angles to validate the 30 degrees. 10 degrees is given.
Draw 2 parallel horizontal lines. One that cuts through the entry point on the left side and one that cuts through the exit point on the right side. Then you can find the angle 3 by making the correct comparisons.
Why would you bother to keep track of the angles' relations to the "horizontal"? It is just as irrelevant as the "base" angles! If you don't have enough points of reference, why not add the North Star or the direction to the bathroom? It seems that the hypothesis is not about refraction, but the refraction on a specific prism on somebody's horizontal desk
Only in this case where we have a prism with a 60 - 60 - 60 angle arrangement. With a different prism, the direction of the normal to the surface will be different.
@@MichelvanBiezen ....our eyes see things that are not realty. For instance....the ship that slowly starts Dissapearing from the horizon....you think it is starting to go down the curvature of the globe. In reality, if you look thru a pair of binoculars the ship is still there. Our eyes can only see so far and we see with a point of perception. We have based how we see things with lens....windows, cameras, etc. Things naturally appear curved. This deception are what a lot of theory's are based on. We look through a telescope and gases that are in the upper stratosphere appear to be globular and isolated. But it just is not so. Continuum....space continuum is Truth. We can measure east to west, and yes we hit an invisible something g that stops us from moving forward. North and south are a different story. From the north and south pole if we continue forward, we are under the same sky, no black outer space. Same oxygen and we just keep moving north we are under the sky with land, vegetation, water. Sounds crazy but Admiral Byrd reached a land mass bigger than the USA about 1,700 miles south of the south pole. And it continues....no ends found yet going north and south.
If you keep track of the ship, you will see that the bottom part of the ship disappears while the top part is still visible. As the ship continues to move farther away less and less of the ship will be visible.
@@MichelvanBiezen ....I wish I could tell you that is true but it simply is not. Depending on how good your binoculars are or how good your telescope is, it never disappear...no part of it. It just gets smaller. I used to believe this place was a globe until I witnessed it with my own eyes. I had forgotten about "point of perspective" !!! It blew my mind...I felt numb and when the shock wore off...I started researching. Now I believe we live on a flat plain . I Love Jesus and there are hundreds of scriptures that say it's flat. When God said, " the Earth is immovable". Well.....then there was the video with Admiral Byrd saying that he went 1,700 miles south of the south pole and hit a land mass bigger than the united states. Then the sealer was a book called, "worlds beyond the poles". It will blow your mind.
4:30 I have a question. How'd you know that broken line was the normal in the other side? Is it just a perpendicular line with respect to the normal line in the left side? Thanks.
Why don't you draw two lines with an angle of 150 degrees between them. Then draw the normal lines and determine the angle between them. You may be surprised with the result. (It actually depends on which angle you are looking at).
+Prof. Some Ting Wong I use the subscripts 1 and 2 for the left side and right side of the first boundary. Thus n1 is the index of refraction of the left side (air) and n2 is the index of refraction of the right side. (glass)
Since it is an equilateral triangle all the interior angles are 60 degrees. 60 + 30 = 90 A line perpendicular with a side will make a 30 degree angle with the horizontal.
I am sure that there are several other ways in which you can explain how to solve this problem. It has been my experience teaching this topic for a very long time, that students learn better with a particular method. That said, no method will be ideal for all students.
WHAT OBJECT OCCUPIES THE MOST SPACE?: The answer, incredibly AND ON BALANCE, is WHAT IS E=MC2 !!!! Here's the full proof and the explanation. The SPACE that surrounds us IS quantum gravitational (ON/IN BALANCE), AS ELECTROMAGNETISM/energy is gravity. Great. Gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE, AS ELECTROMAGNETISM/energy is gravity; AS WHAT IS E=MC2 is taken directly from F=ma; AS “mass”/energy is CLEARLY electromagnetic/gravitational ON/IN BALANCE; AS TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE. Great. To answer the question: “What is nothing in accordance with physics (AND TIME)?”, we must understand (ON BALANCE) WHAT IS SOMETHING; AS BALANCE AND completeness go hand in hand. The ultimate unification and understanding of physics/physical experience (AND TIME) combines, BALANCES, AND INCLUDES opposites. Carefully consider what is THE EYE (ON BALANCE). Do notice the associated black “space” AND the dome AS WELL. NOW, carefully consider what follows !!!! The following proves what is the fourth dimension ON BALANCE. WHAT IS E=MC2 is the fundamental basis for the true understanding of what is inertia/INERTIAL RESISTANCE. TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE, AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE). INDEED, consider TIME AND time dilation ON BALANCE !!!! (The stars AND PLANETS are POINTS in the night sky ON BALANCE.) REGARDING WHAT IS E=MC2, c squared CLEARLY AND NECESSARILY represents a dimension of SPACE ON BALANCE. INDEED, consider what is THE EYE ON BALANCE; AS two AND three dimensional SPACE are, in fact, BALANCED !!!! Great. What is gravity is, ON BALANCE, an INTERACTION that cannot be shielded or blocked. Consider what is the ORANGE AND setting SUN. Notice what is the fully illuminated (AND WHITE) MOON. It is the same size as what is THE EYE. Notice what is the TRANSLUCENT AND BLUE sky. Indeed, consider complete combustion !!!! (I have mathematically proven the fourth dimension.) The density of what is pure WATER IS HALF of that of what is packed sand/wet packed sand. Now, WHAT IS THE EARTH IS ALSO BLUE !!!! The rotation of WHAT IS “THE MOON” matches the revolution, AS ELECTROMAGNETISM/energy is CLEARLY (AND NECESSARILY) proven to be gravity (ON/IN BALANCE) !!!! CLEARLY, gravity AND ELECTROMAGNETISM/energy are linked (AND BALANCED) opposites (ON BALANCE); as the stars AND PLANETS are POINTS in the night sky. Consider TIME AND time dilation ON BALANCE. CLEARLY, ON BALANCE, I have solved WHAT IS the coronal heating “problem”. GREAT. (Indeed, consider what is lightning.) Absolute SPACE IS the truly and fundamentally BALANCED inertial frame (or SPACE). Indeed, “mass”/ENERGY is CLEARLY electromagnetic/gravitational ON/IN BALANCE; AS c squared CLEARLY (AND NECESSARILY) represents a dimension of SPACE (ON BALANCE) REGARDING WHAT IS E=MC2. INDEED, consider TIME AND time dilation ON BALANCE; AS this proves what is the FOURTH dimension. Consider what is the man (AND THE EYE ON BALANCE) who IS standing on what is THE EARTH/ground. Great !!!! Think. The fourth dimension AND WHAT IS E=MC2 are FUNDAMENTALLY consistent with/AS what are wave/particle duality AND the fact that c squared CLEARLY (AND NECESSARILY) represents a dimension of SPACE ON BALANCE (REGARDING WHAT IS E=MC2) !!!! CLEARLY (ON BALANCE), gravity AND ELECTROMAGNETISM/energy are linked AND BALANCED opposites; as the stars AND PLANETS are POINTS in the night sky ON BALANCE !!!! INDEED, consider TIME AND time dilation ON BALANCE; AS “mass”/ENERGY is (CLEARLY) electromagnetic/gravitational ON/IN BALANCE; AS TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE; AS the rotation of WHAT IS THE MOON matches the revolution; AS WHAT IS E=MC2 is taken directly from F=ma; AS ELECTROMAGNETISM/energy is CLEARLY (AND NECESSARILY) proven to be gravity (ON/IN BALANCE) !!!! CLEARLY (ON BALANCE), I have mathematically proven and explained what is the FOURTH dimension; AS TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE. INDEED, consider TIME AND time dilation ON BALANCE; AND consider what is complete combustion (ON BALANCE); AS ELECTROMAGNETISM/energy is CLEARLY (AND NECESSARILY) proven to be gravity (ON/IN BALANCE) !!!! Great. It is proven. Finally, ON BALANCE, notice WHAT IS the TRANSLUCENT AND BLUE sky. Magnificent !!!! Think. It all CLEARLY makes perfect sense ON BALANCE !!!! Notice WHAT IS “THE MOON” (ON BALANCE) !!!! THINK !!!! ABSOLUTELY MAGNIFICENT !!!! CONSIDER TIME AND TIME DILATION ON BALANCE !!!! GREAT !!!! AGAIN, do notice WHAT IS the ORANGE “SUN” ON BALANCE !!!! Great. It ALL CLEARLY makes perfect sense ON BALANCE. By Frank Martin DiMeglio
I thought no other tutor could ever explain better than the organic chemistry tutor....but you are one of a kind sir💯💯
Happy to help
After doing these calculations a few times, I noticed that for a 60 degree equilateral prism, the two angles inside the prism (theta 2 and theta 3) add up to 60. Nice little shortcut for equilateral prisms--less geometry!
That is a good shortcut. We like to show the general method that works in all cases.
just about to take my aqa A level physics exam tomorrow and came across your workthroughs for difficult refraction and TIR problems, just what i needed! been stuggling on more complex ones like these for a while and you have helped me alot with this topic! a big thanks to your physics and mathematics playlists, cant wait to see more vids in the future!
All the best on your exam.
The video is 1st class, excellent explanation and the quality of the overall video is just wow.
This is challenging! I rewatched twice to fully understand. What is difficult in my opinion is knowing to replicate the horizontal beneath the refracted light once more and knowing it is also 30 degrees because it was the angle between the medium and horizontal coming in on the left side, then adding the 5.7 degrees to that because of the reflected angle.
THANK YOU SO MUCH. This made so much more sense after you went step by step and showed which angles were relative to which normal.
cool fact:If you transpose the light beam such that the normal entry line intersects with one corner of the prism, you can apply angle sum of triangle twice to find the 35.7 deg
Great input! 🙂
Thanks, this is by far the best prism lesson I've found :)
Sir has helped me to a greater extent
Glad to hear it. 🙂
@@MichelvanBiezen all your physics videos actually interpret my syllabus 😊
thank you very much sir for the video I understand after seeing this video but I have a question 1,56where did you get it from? Thank you in advance sir 🙏🏻
That is a given. The index of refraction of glass varies from about 1.5 to about 1.6
thank you so much i watched a lot of videos and none of them explained it like you did! i understand now
Glad it helped! 🙂
prof Biezen you are the best
Glad you are enjoying our videos. 🙂
What should you do if nsin(theta) is greater than 90.
Depends on which "n sin(theta)" you are referring to. If you are referring to the exiting ray, then you'll have internal reflection. (see the videos on total internal reflection)
What should I do if theta 3 is about 40° or bigger? with that IOR, 1.56 * sin(40°) = 1.002... => arcsin from something > 1 isn't possible. Is there a different approach?
Then there will be total internal reflection on that boundary and the ray will not leave the prism at that location.
How did you find out the 10 degrees and 30 degrees on the angle of incidence?
Im sure you figured this out by now but I had the same issue. For anyone new: the line perpendicular to the surface has one 90 degree angle. then if you draw a line perpendicular to the bottom of the triangle you can use a combination of complimentary and supplementary angles to validate the 30 degrees. 10 degrees is given.
is there a way to find the result without using a calculatrice ?? btw thanks for the explanation god bless youu
Wonderful video
Many thanks
Theta2 + Theta3 is always equal to the top angle of the prism right?
That appears to be correct. A good way to check is to let the top angle go to zero and then to 180 degrees to see if that holds true.
How did you know what angle theta sub 3 was?
Draw 2 parallel horizontal lines. One that cuts through the entry point on the left side and one that cuts through the exit point on the right side. Then you can find the angle 3 by making the correct comparisons.
How do I find the angle of Theta3 if the prism is not equilateral?
The technique would be the same. I probably should add a few more examples. This playlist may help: PHYSICS 51 LIGHT REFLECTION
Why would you bother to keep track of the angles' relations to the "horizontal"? It is just as irrelevant as the "base" angles!
If you don't have enough points of reference, why not add the North Star or the direction to the bathroom?
It seems that the hypothesis is not about refraction, but the refraction on a specific prism on somebody's horizontal desk
i still don't get , how you find third angle
Requires geometry by knowing that a right triangle is 180 degrees. The video over-complicated it for this problem, IMO.
listen its not that hard .angle 3 u just add the thirty degrees plus the angle below the horizontal (5.7) amd u get ur answer
thank you for all your great lessons!
do u have a lesson for Angle of devitation?
No we don't. We will add it to the list of topics to cover.
theta sub 2 + theta sub3 = deviation angle, in this case 24.3 + 35.7 = 60, sorry 5 years late
how can we theoretically prove that the 24.3 degrees is above the normal rather than below it? I only know this from experience.....
I think I get why it bends either towards or away from normal now. Got to do with Maxwell's law
Does the normal always make an angle of 30 degrees with the horizontal??
Only in this case where we have a prism with a 60 - 60 - 60 angle arrangement. With a different prism, the direction of the normal to the surface will be different.
Michel van Biezen Ok.. Thank you sir.. :)
What happens if the lens is deceptive ? If the lens is deceptive...the entire theory and answers to the theory would be incorrect....right ?
What do you mean by "the lens is deceptive"?
@@MichelvanBiezen ....our eyes see things that are not realty. For instance....the ship that slowly starts Dissapearing from the horizon....you think it is starting to go down the curvature of the globe. In reality, if you look thru a pair of binoculars the ship is still there. Our eyes can only see so far and we see with a point of perception. We have based how we see things with lens....windows, cameras, etc. Things naturally appear curved. This deception are what a lot of theory's are based on. We look through a telescope and gases that are in the upper stratosphere appear to be globular and isolated. But it just is not so. Continuum....space continuum is Truth. We can measure east to west, and yes we hit an invisible something g that stops us from moving forward. North and south are a different story. From the north and south pole if we continue forward, we are under the same sky, no black outer space. Same oxygen and we just keep moving north we are under the sky with land, vegetation, water. Sounds crazy but Admiral Byrd reached a land mass bigger than the USA about 1,700 miles south of the south pole. And it continues....no ends found yet going north and south.
If you keep track of the ship, you will see that the bottom part of the ship disappears while the top part is still visible. As the ship continues to move farther away less and less of the ship will be visible.
@@MichelvanBiezen ....I wish I could tell you that is true but it simply is not. Depending on how good your binoculars are or how good your telescope is, it never disappear...no part of it. It just gets smaller. I used to believe this place was a globe until I witnessed it with my own eyes. I had forgotten about "point of perspective" !!! It blew my mind...I felt numb and when the shock wore off...I started researching. Now I believe we live on a flat plain . I Love Jesus and there are hundreds of scriptures that say it's flat. When God said, " the Earth is immovable". Well.....then there was the video with Admiral Byrd saying that he went 1,700 miles south of the south pole and hit a land mass bigger than the united states. Then the sealer was a book called, "worlds beyond the poles". It will blow your mind.
4:30 I have a question. How'd you know that broken line was the normal in the other side? Is it just a perpendicular line with respect to the normal line in the left side? Thanks.
parallel to the first normal
You are a great teacher and person! Thank you
We appreciate the comment.
Isn't the wavelength of the electromagnetic wave (light) also a factor of the angle of refraction?
You are correct, the angle of refraction does depend on the wavelength.
Thank you sir❤
You are welcome. 🙂
thank you so much for the great guide,couldnt find any better than this
Do buggy high by for her that end
Many thanks!
Many welcomes!
sir you are awesome you are amazing you explain concept in a very easy way you are great sir hats of to you
I'm doing my gcses in less than 40 days wish me luck!! I really need to :D
Not sure what that is, but good luck! 🙂
Thanks
Welcome
Thanks a lot
Happy to help
sooo helpful
Glad you think so! 🙂
The angle between two lines is the same as the angle between their normal right?
Why don't you draw two lines with an angle of 150 degrees between them. Then draw the normal lines and determine the angle between them. You may be surprised with the result. (It actually depends on which angle you are looking at).
What is N1 and how did you calculate N2?
+Prof. Some Ting Wong
I use the subscripts 1 and 2 for the left side and right side of the first boundary. Thus n1 is the index of refraction of the left side (air) and n2 is the index of refraction of the right side. (glass)
that was slightly unclear but thanks for a very detailed presentaion otherwise.This clarified most of my doubts on this topic :-)
you are truly great
How did you get n1 to equal 1 and n2 to equal 1.56?
n1 is the index of refraction outside the prism and n2 is the index of refraction inside the prism
Different materials have different properties. google "index of refractions". Example: Water N2=1.33 Epoxy N2=1.55
THANK YOU SO MUCH!! this makes so much sense after you went through it step by step, I will never figure this out by my own :(
Glad it helped! Once you see the "trick" of how to look at the angles it becomes easy,
i mean how you get 30, in theta3 = 30 + 5.7
Since it is an equilateral triangle all the interior angles are 60 degrees. 60 + 30 = 90 A line perpendicular with a side will make a 30 degree angle with the horizontal.
This is the reason why we must always review the BASICS of Geometry and Trigonometry.
Knowing geometry and trigonometry well helps immensely with these types of problems.
I know it's not relevant, but, he sounds exactly like Gru from Despicable Me.
this is awesome thanks a lot teacher
not very clear to find the angles
Very clear. Thank you Sir
This overcomplicates Snell's Law completely
Then this video is not meant for you, there are beginners friendly videos too
Better explained impossible, congrats
Glad you think so!
Thank you very much . very helpful
thanks sir ur epic
why bother talking about the horizontal line so much when angles of a triangle can be calculated with more basic rules... convoluted explanation..
I am sure that there are several other ways in which you can explain how to solve this problem. It has been my experience teaching this topic for a very long time, that students learn better with a particular method. That said, no method will be ideal for all students.
how angle 2 and angle 3 can be different?
Because the opposite sides of the prism are not parallel.
That's amazing! Thanks
thanks a lot mate🙏🙏
thank you!
nice lesson teacher but the video not clear.........like your exeplanation
bowties are cool
bantikive vurum
WHAT OBJECT OCCUPIES THE MOST SPACE?:
The answer, incredibly AND ON BALANCE, is WHAT IS E=MC2 !!!! Here's the full proof and the explanation.
The SPACE that surrounds us IS quantum gravitational (ON/IN BALANCE), AS ELECTROMAGNETISM/energy is gravity. Great.
Gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE, AS ELECTROMAGNETISM/energy is gravity; AS WHAT IS E=MC2 is taken directly from F=ma; AS “mass”/energy is CLEARLY electromagnetic/gravitational ON/IN BALANCE; AS TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE. Great.
To answer the question: “What is nothing in accordance with physics (AND TIME)?”, we must understand (ON BALANCE) WHAT IS SOMETHING; AS BALANCE AND completeness go hand in hand. The ultimate unification and understanding of physics/physical experience (AND TIME) combines, BALANCES, AND INCLUDES opposites. Carefully consider what is THE EYE (ON BALANCE). Do notice the associated black “space” AND the dome AS WELL. NOW, carefully consider what follows !!!! The following proves what is the fourth dimension ON BALANCE.
WHAT IS E=MC2 is the fundamental basis for the true understanding of what is inertia/INERTIAL RESISTANCE. TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE, AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE). INDEED, consider TIME AND time dilation ON BALANCE !!!! (The stars AND PLANETS are POINTS in the night sky ON BALANCE.) REGARDING WHAT IS E=MC2, c squared CLEARLY AND NECESSARILY represents a dimension of SPACE ON BALANCE. INDEED, consider what is THE EYE ON BALANCE; AS two AND three dimensional SPACE are, in fact, BALANCED !!!! Great. What is gravity is, ON BALANCE, an INTERACTION that cannot be shielded or blocked. Consider what is the ORANGE AND setting SUN. Notice what is the fully illuminated (AND WHITE) MOON. It is the same size as what is THE EYE. Notice what is the TRANSLUCENT AND BLUE sky. Indeed, consider complete combustion !!!! (I have mathematically proven the fourth dimension.) The density of what is pure WATER IS HALF of that of what is packed sand/wet packed sand. Now, WHAT IS THE EARTH IS ALSO BLUE !!!! The rotation of WHAT IS “THE MOON” matches the revolution, AS ELECTROMAGNETISM/energy is CLEARLY (AND NECESSARILY) proven to be gravity (ON/IN BALANCE) !!!! CLEARLY, gravity AND ELECTROMAGNETISM/energy are linked (AND BALANCED) opposites (ON BALANCE); as the stars AND PLANETS are POINTS in the night sky. Consider TIME AND time dilation ON BALANCE. CLEARLY, ON BALANCE, I have solved WHAT IS the coronal heating “problem”. GREAT. (Indeed, consider what is lightning.)
Absolute SPACE IS the truly and fundamentally BALANCED inertial frame (or SPACE). Indeed, “mass”/ENERGY is CLEARLY electromagnetic/gravitational ON/IN BALANCE; AS c squared CLEARLY (AND NECESSARILY) represents a dimension of SPACE (ON BALANCE) REGARDING WHAT IS E=MC2. INDEED, consider TIME AND time dilation ON BALANCE; AS this proves what is the FOURTH dimension. Consider what is the man (AND THE EYE ON BALANCE) who IS standing on what is THE EARTH/ground. Great !!!! Think. The fourth dimension AND WHAT IS E=MC2 are FUNDAMENTALLY consistent with/AS what are wave/particle duality AND the fact that c squared CLEARLY (AND NECESSARILY) represents a dimension of SPACE ON BALANCE (REGARDING WHAT IS E=MC2) !!!! CLEARLY (ON BALANCE), gravity AND ELECTROMAGNETISM/energy are linked AND BALANCED opposites; as the stars AND PLANETS are POINTS in the night sky ON BALANCE !!!! INDEED, consider TIME AND time dilation ON BALANCE; AS “mass”/ENERGY is (CLEARLY) electromagnetic/gravitational ON/IN BALANCE; AS TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE; AS the rotation of WHAT IS THE MOON matches the revolution; AS WHAT IS E=MC2 is taken directly from F=ma; AS ELECTROMAGNETISM/energy is CLEARLY (AND NECESSARILY) proven to be gravity (ON/IN BALANCE) !!!! CLEARLY (ON BALANCE), I have mathematically proven and explained what is the FOURTH dimension; AS TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE. INDEED, consider TIME AND time dilation ON BALANCE; AND consider what is complete combustion (ON BALANCE); AS ELECTROMAGNETISM/energy is CLEARLY (AND NECESSARILY) proven to be gravity (ON/IN BALANCE) !!!! Great. It is proven. Finally, ON BALANCE, notice WHAT IS the TRANSLUCENT AND BLUE sky. Magnificent !!!! Think. It all CLEARLY makes perfect sense ON BALANCE !!!! Notice WHAT IS “THE MOON” (ON BALANCE) !!!! THINK !!!! ABSOLUTELY MAGNIFICENT !!!! CONSIDER TIME AND TIME DILATION ON BALANCE !!!! GREAT !!!! AGAIN, do notice WHAT IS the ORANGE “SUN” ON BALANCE !!!! Great. It ALL CLEARLY makes perfect sense ON BALANCE.
By Frank Martin DiMeglio
thanks