Using ray diagrams to better understand everyday reality – Demo

One of the easiest way to visualize ray diagrams for lenses is by using an array of arrows on the board as the object and the camera on your phone as the screen.

(i) Convex Lens : Arrows on the board are placed outside the focal length of the lens -> Inverted image

(ii) Convex Lens :Arrows on the board are placed inside the focal length of the lens -> Magnified Erect image

(iii) Concave Lens: Irrespective of whether you place the arrows inside or outside the focal length, you get an erect image.

(iv) Convex mirror: Virtually erect image formed from a Christmas ornament

The following video from UCLA extends the ray diagram analysis for concave and convex mirrors:

Physics of invisibility

(This page will be updated as the quarter progresses with other techniques that you will eventually learn about)

There are many way to make things “disappear” and impart the illusion of invisibility. Based on what you have studied so far, here is one possible ways you can do so. (There are certainly other ways and I strongly recommend spending some time thinking about this)

Using the refractive index

If you want to make something invisible,you have to ensure that the index of refraction of the object and the medium where you are hiding it remain the same and also that the object is transparent and colorless.

The refractive index of a polymer ball is identical to that of water and if you immerse a colorless polymer ball in water, you can make it ‘disappear’ like the animation above shows you.

When you immerse colored polymer balls in water on the other, they seem as if they are 2-d objects although they are spheres!

Van Gogh’s The Starry Night, Turbulence and Adaptive optics

Van Gogh’s The Starry Night is a stunning painting that artistically brings out the effect of turbulence in our atmosphere.

And this turbulence of air in addition to the effect of varying refractive index of the layers in our atmosphere causes the twinkling of stars:

If you are an astronomer trying to study the cosmos from the earth, this turbulence of air and twinkling of stars is a total nightmare.

The last thing that you want the light that painstakingly took millions of years to get to the earth is to be wiggled away from your telescope through refraction and turbulence!

But Astronomers found a way to deal with this, a technique called ‘Adaptive Optics’ which uses deformable mirrors to account for the disturbances in the atmosphere.

Using this technique, the following is the difference between capturing an image with and without adaptive optics.

What can you find with this technique?

Here’s an interesting question: What exactly is at the center of our galaxy? Is there a black hole ? How do we go about studying it?

Prof.Andrea Ghez and her research group at the UCLA’s Galactic center group were inspired by the same question and decided to look at a region in the sky which they believed was the center of our milky way galaxy.

And this is what they found of the trajectories of stars surrounding the proposed center of the galaxy:

The first thing that you notice about these stars is that they are orbiting a point in space. This is very similar of how planets in our solar system are orbiting the sun.

One of the special stars in that animation is S0-2 which completes its elliptical orbit in only 15 years!

( it takes the sun approximately 225-250 million years to complete one journey around the galaxy’s center )

But having this knowledge of how small the orbit is, we can use Kepler’s law to find out the Mass at the center of the galaxy. And we get the mass of the center of our galaxy as a staggering 4 million times the mass of the Sun

How massive is that?

Let’s take a look at the orbits once again:

The radius of this object at the center, in order to avoid collision with the rest of the objects has to be about the diameter of Uranus’s orbit.

So, an object that has 4 million times the mass of the Sun. and diameter of Uranus’s orbit .. Hmm.. The only astronomical object that would fit this characteristic is a Super Massive Black Hole (SMBH)

And that’s why we believe that at the center of our galaxy is a SMBH: Something we would not have been able to realize without adaptive optics.

So, the next time you go out to gaze at the cosmos, just remember that whatever you are seeing in the night sky right now is through the looking glass of our beloved atmosphere.

And astronomers put in immense effort to nullify the dynamic atmospheric effects that it loves to entertain us with.

All images/animations featured in this post were created by Prof. Andrea Ghez and her
research team at UCLA and are from data sets obtained with the W. M.
Keck Telescopes