How to photograph shock waves ?

fyfd:

This week NASA released the first-ever image of shock waves interacting between two supersonic aircraft. It’s a stunning effort, requiring a cutting-edge version of a century-old photographic technique and perfect coordination between three airplanes – the two supersonic Air Force T-38s and the NASA B-200 King Air that captured the image. The T-38s are flying in formation, roughly 30 ft apart, and the interaction of their shock waves is distinctly visible. The otherwise straight lines curve sharply near their intersections. 

Fully capturing this kind of behavior in ground-based tests or in computer simulation is incredibly difficult, and engineers will no doubt be studying and comparing every one of these images with those smaller-scale counterparts. NASA developed this system as part of their ongoing project for commercial supersonic technologies. (Image credit: NASA Armstrong; submitted by multiple readers)

How do these images get captured?

It may not obvious as to how this image was generated because if you have heard about Schlieren imaging what you have in your head is a setup that looks something like:

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But how does Schelerin photography scale up to capturing moving objects in the sky?

Heat Haze

When viewing objects through the exhaust gases emanating from the nozzle of aircrafts, one can observe the image to be distorted.

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Hot air is less dense than cold air.

And this creates a gradient in the refractive index of the air

Light gets bent/distorted

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Method-01 : BOSCO ( Background-Oriented Schlieren using Celestial Objects )

You make the aircraft whose shock-wave that you would like to analyze pass across the sun in the sky.

You place a hydrogen alpha filter on your ground based telescope and observe this:

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                  Notice the ripples that pass through the sunspots

The different air density caused by the aircraft bends the specific wavelength of light from the sun. This allows us to see the density gradient like the case of our heat wave above.

We can now calculate how far each “speckle” on the sun moved, and that gives us the following Schlieren image.

Method-02: Airborne Background Oriented Schlieren Technique

In the previous technique how far each speckle of the sun moved was used for imaging. BUT you can also use any textured background pattern in general.

An aircraft with camera flies above the flight like so:

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The patterned ground now plays the role of the sun. Some versions of textures that are commonly are:

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The difficulty in this method is the Image processing that follows after the images have been taken. 

And one of the main reasons why the image that NASA has released is spectacular because NASA seems to have nailed the underlying processing involved.

Have a great day!

* More on Heat hazes

** More on BOSCO

*** Images from the following paper : Airborne Application of the Background Oriented Schlieren Technique to a Helicopter in Forward Flight

**** This post obviously oversimplifies the technique. A lot of research goes into the processing of these images. But the motive of the post was to give you an idea of the method used to capture the image, the underlying science goes much deeper than this post.

n roots of unity

When one is dealing with complex numbers, it is many a times useful to
think of them as transformations. The problem at hand is to find the n
roots of unity. i.e

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As is common knowledge z = 1 is always a solution.

Multiplication as a transformation

Multiplication in the complex plane is mere rotation and scaling. i.e

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Now what does finding the n roots of unity mean?

If
you start at 1 and perform n equal rotations( because multiplication is nothing but rotation + scaling ), you should again end up
at 1.

We just need to find the complex numbers that do this.i.e

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This implies that :

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And therefore :

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Take a circle, slice it into n equal parts and voila you have your n roots of unity.

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Okay, but what does this imply ?

Multiplication by 1 is a 360o / 0o rotation.

When
you say that you are multiplying a positive real number(say 1) with 1 ,
we get  a number(1) that is on the same positive real axis.

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Multiplication by (-1) is a 180o rotation.

When you multiply a positive real number (say 1) with -1, then we get a number (-1) that is on the negative real axis 

The act of multiplying 1 by (-1) has resulted in a 180o transformation. And doing it again gets us back to 1.

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Multiplication by i is a 90o rotation.

Similarly multiplying by i takes 1 from real axis to the imaginary axis, which is a 90o rotation. 

This applies to -i as well.

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so on and so forth,

Have a great day!

The size of things

Sometimes I feel like we don’t appreciate how much we have evolved in technology only in the past few decades.

Centrifugal force and seat belts

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The basic
concept of a seatbelt is to protect you in an automobile collision by
holding you in your seat. This prevents you from flying forward and
colliding with the dashboard or windshield.

How do you do that ?

Many common seat belts design have something known as a centrifugal clutch. This arrangement has a weight attached to the end of a spool

When the spool rotates at a low speed, the weight is held through spring action and is allowed to spin freely.

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But you must have noticed that if you try to pull the seat belt faster then it kinda gets stuck.

This is because as you rotate the spool faster, centrifugal force causes the weight to be pushed out and that stops the spool from rotating further.

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This adds tension to your seat belt and holds you to your seat at the time of a crash. 

Have a great day!

* Other seatbelt mechanisms

** Seatbelt physics

fuckyeahphysica:

That’s Electrooculography!

The eye is a basically a dipole ( a separation of electric charges )

It was observed by Reymond in 1848 that the cornea of the eye is electrically positive relative to the back of the eye.This potential was surprisingly not dependent on the amount of light falling on the eye.

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                The cornea is the transparent front part of the eye

Dipoles and Eye Tracking

This means that as the eye moves from side to side, the dipole moves as well. To capture the movement of the dipole, one places two electrodes on both sides of the eye. ( like the one placed on this guy )

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If the eye moves from the center position to the right, one of the electrodes becomes slightly positive and the other negative. This leads to a spike in the positive direction.

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                                                  Source

And if the eye moves from the center position to the left, the polarity of the electrodes reverses. This leads to a spike in the negative direction.

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That’s about it. That’s EOG for you all. I hope you guys enjoyed this post.

Have a great day!

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Sources and Extras:

More about EOG

Gif source : The backyard brains

Up and Down

You can also measure upwards and downwards motion of the eye using the same EOG. And you do that by placing the electrodes on the top and bottom of the eye. ( It works the same way )

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Application to VR

Guys, there are lot of people working on interfacing VR with EEG/EOG/ECG. ( Read more ). Hang tight 😀

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The holy grail of Electromagnetic Radiation

James Clark Maxwell’s theory of electromagnetism was published in 1865.

And one of the most crucial prediction that was made is that so called Electromagnetic waves existed and they moved at the speed of light ( and light was one such wave ).

Experimentalists around the world got to work to seek these waves and Heinrich Hertz was one of the first ones to verify maxwell’s predictions.

The discovery of EMW

The setup that Hertz used is shown below.

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                         Original source of image : DMGualtieri

Transmitter

The crux of transmitter setup is the spark gap. Think of this as the spark plug that is used in your vehicles and how the electrons jump across the air gap due to the high electric field

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                                                Source

Now, by using Capacitors and Inductors Hertz was able to alter the frequency of oscillation of this spark between the gap. These are known as L-C oscillations. ( Click here to know more on how they work )

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                                                  Source

Receiver

He just used a copper wire and bent it into a circle and placed 2 small brass spheres at each end.

Goddamn it, What happened ?                                         

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                                     Source: The secret life of machines

According to Maxwell’s theory, if electromagnetic
waves
were spreading from the oscillator sparks, they would induce a current
in the loop that would send sparks across the gap.

This was exactly what occurred when
Hertz
turned on the oscillator, producing the first transmission and
reception
of electromagnetic waves

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.

‘Sparked’ an innovation frenzy

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In this experiment Hertz confirmed Maxwell’s theories about the existence of electromagnetic radiation and also inadvertently inspired the invention of the Wireless Telegraph, Radio, TV and others.  

For this remarkable contribution, the SI unit of frequency has been named ‘Hertz’ in his honor.

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Thus, Physicists at the end of the 1900s had a new toy to play around with – Electromagnetic Waves !

Have a great day!

10 Secret Trig Functions Your Math Teachers Never Taught You

curiosamathematica:

On Monday, the Onion reported that the “Nation’s math teachers introduce 27 new trig functions”. It’s a funny read. The gamsin, negtan, and cosvnx from the Onion article are fictional, but the piece has a kernel of truth: there are 10 secret trig functions you’ve never heard of, and they have delightful names like ‘haversine’ and ‘exsecant’.

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Trigonometry and its weird names have baffled me for ages. I decided to put an end to this madness by trying to understand them ;P

Here is my interpretation on what thy mean. You can find a detailed etymology here.

Sine

Sine ( meaning ~ bowstring in sanskrit  )is ratio of the length of the bowstring with the diameter of the circle that the bow makes.

Sin(theta) because this ratio is solely dependent on the angle ‘theta’. Even the slightest change in theta messes up this ratio.

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So, when theta = 90 (or 2*theta = 180) , we can see that x = d. This is why sin(90)= 1.

Cosine

‘Compliment sine’ ( ratio in the perpendicular direction of sine )

Cosine is the ratio of the distance between the bowstring and the center of the bow circle to the diameter of the circle.

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So, when theta = 0 , we can see that y = d. This is why cos(0)= 1.

Sine2 + cosine 2 = 1 ?

Well.. thats because of our old friend Pythagoras

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Have a great day!

10 Secret Trig Functions Your Math Teachers Never Taught You

Colors are nature’s way of expressing beauty. And we often find ourselves in this situation where we want to capture this ecstasy. A camera rose out of this innate longing to capture and invariably store these memories.

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Generally when people are on the lookout for buying new phones/cameras, one of the parameters that is looked into is the MP(Megapixels) of the camera.

2.0 MP means that there are ~2million ‘effective’ pixels on the image that has been captured. *

But,what is a pixel ?

Pixel ( or picture element ) is a small element on the screen that represents a specific color. 

But how do you represent any color – with the primary color system of course!! Add the red, blue and green in varying proportions and voila! you can span the entire color spectrum. **

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Therefore,every pixel is constituted of 3 ‘compartments’ – Red, Green and Blue to produce the necessary color distribution of an image.

The subtlety of a screen

Wait!! Hold on are you saying that there are millions of red, green and blue lights on my screen ?

Don’t believe me ? Take a took at these images of a smart phone screen under 30x and 60x magnification.

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                  One RGB block is called a pixel. Video Source : Microworld

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Now this ‘array type of arrangement’ is not necessarily the case with all manufacturers.

In fact, most manufacturers have their own unique type of representation ( see below )and the type varies with the type of application as well.

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                                Photo credit: Peter Halasz. (User:Pengo)

If you have a tough time realizing how a set of RGB lights flashing on a screen is able to project a crisp image, then try this out:

Turn an excel sheet into an image

On the fundamental level, yes! it is merely a set of lights.

But once you start stacking a lot of these pixels next to one other in a grid ( 2 million of them for a 2.0 MP camera! ), you can start to see how a beautiful image emerges out.

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Convert any image to a excel sheet here and explore !

To think that are millions of pixels on the screen rendering the plethora of images that I behold everyday BLOWS my mind out of proportions ;D
Have a great day!


Do more megapixels mean better picture quality ? Sort of but not always!

** What is additive color mixing ? Its not the same as you do with paint!

Adieu 2016 – Best of FYP!

2016 has been a great year for FYP!

And we would like to conclude it with some of the best posts that we have been able to produce

1. Black hole are not so black – series

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Part – I , II, III

2.‘Katana’ – A sword that can slice a bullet

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3. A denied stardom status – Jupiter

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4. The Pythagoras Cup

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5. On Pirates and Astronomers
                                                          

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6. Behold- The Space Shuttle Tile

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7. Principle of Least Effort

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8. Leidenfrost Effect

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9. Major Types of Engines

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10. A holy matrimony of Pascals and Sierpinski’s Triangle

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11. Curves of constant width

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12. Smooth Ride, Bumpy Road

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Thank you so much following us ! Have a great weekend 😀

 – Fuck Yeah Physics!

Divisibility tests exposed!

Number theory is the home to a
myriad of beautiful proofs, and let’s set forth on this journey by
learning about divisibility tests.

Have a great day!