We were discussing the topic of light
concentration, and in one of the previous videos.
I derived this formula for the concentration
that you can achieve in a system like
this, and I'd relate it, essentially, to the
incidence angle of my of my incoming light.
Which was, I defined it as alpha, and then the
final angle on which, the angle at which this, this.
The light which is concentrated hits this disc one which I
will concentrate my light and I had essentially pointed out that.
it's proportionally to the sine squared of this angle of incidence on
my finger disc and it's inversely proportional to the sine squared.
Of this, of this angle at which my, light is hitting my, receptor.
Then
I had, further commented that, this, this concentration would be
maximum when, essentially, this, this sine score beta is maximum.
And that would be the case when this beta is
90 degree, or this two beta is equal to 180 degree.
So the maximum concentration, what it means is that
it would be achieved when this incoming light is essentially
just hitting this final disc at a grazing angle essentially.
It's hitting this disc at this angle of of two
beta 180 or beta of 90 degree which cooresponds to.
this grazing incidents, and you can see that would be the point
where this finer disc is collecting as much light as it can.
So, it's collecting all the light,
all the way to this grazing angle. And that gave me the value of maximum
concentration to be equal to n squared divided by sine squared alpha.
And then for this alpha would be
essentially the minimum this can be would be
related to the emulate what the angle, the angle of the of the cone, which substains
[INAUDIBLE].
So this, the minimum value of p
[UNKNOWN],
for concentrating sunlight would be equal. The minimum value of this alpha
would be equal to this angle that the sun sustains at a point so it's
[UNKNOWN].
And that is equal to 27 degree and that give me maximum value of my concentration.
But most of the systems that people are concentrated light systems that people
used for concentrated photo voltaic or
even solar thermal or concentrated solar power.
They operate at concentrations much lower than this much
lower than this theoretical maximum and you can kind
of see the reason for that from this this simple equation again.
And I can write, rewrite these simple equations where
I can take this denominator over here to this side.
I can, I can rewrite this as, as essentially my concentration, multiplied
by sin squared alpha, has to be equal to n squared sine square beta.
And then I can further say that this sine squared beta, it's always it will
[INAUDIBLE]
between 0 and 1. So I can say that my concentration
multiplied
by And so
essentially
if I
increase my concentration,
I will require
a very very
good tracking.
So I require a very good tracking for this high concentration system.
Another way to think about this signs this alpha, is to think
many people you know, think about it, or call that, they refer.
For this is an acceptance angle and that is shown over here.
So let's say you know I have light
incident at at a particular angle which is very
close to my normal.
And then I have this lens which is concentrating
this light onto this disc which has a radius r.
So in this slice is close to, close to my normal incidence, this
this would be essentially way closer to the center of this of this smaller disc.
But as I try to increase the angle of
this incoming light, I see that I've essentially, you know,
this this focused part will move towards the edge of the disc.
And if I increase this angle furthermore, then you
see that my focal point is essentially out of this
[UNKNOWN].
So I essentially I can call this
angle, this maximum angle, which is allowed, before
this light moves away from the small disc, on which I were to concentrate my light.
I call this angle typically as my acceptance angle.
So with that equation I, I can again restate that
as essentially my concentration multiplied by essentially sin square of my
This acceptance angle has to be less than less
then n square, or less than equal to n square.
So whenever I'm increasing my concentration, I'm decreasing this.
It's acceptance angle.
So I require a very precise tracking, and that essentially
many times limit the maximum value of concentration I can achieve.
Now, another thing I want to mention, and
if you read papers about these about these
concentrated systems or you read articles about them.
A term that you will often find mentioned in this imaging versus non-imaging optics.
And I will illustrate that by using the case of this parabolicness.
So the first thing that might come to your mind if
you think about, you know how do I design a concentrator?
So you
might think that I can take this parabolic, or this circular mirror,
and I can use it essentially to concentrate this sunlight
from sun. Onto this small disc, so the small disc
has a radius of A, and this big parabolic has a, let's say It has this
area which has odameter of 2D radius of D. So I can
see that for this system, this is I can see that this is an imaging system
essentially this parabolic disk will focus all the parabolic beams of light
to the focal point at which I Place my disk so that this light
which is coming exactly parallel will essentially
get focused at the centre of this disc.
And this light which are essentially since sun is not exactly a point so
as this light is coming in this cone with this solid
angle theta s, so you see that this side of the cone.
Or, you know, these two sides of the cone, they
will get projected on these two edges of this disc.
And you'll obtain essentially this image of my image of the sun.
So if you essentially, you know, look into this disc, and I don't
advise doing so because it would be.
Very highly concentrated and previously, you know, generations of astronomers have
tried that and there is a serious possibility of going blind, but anyway.
If you are wearing glasses and you do look over here,
you see essentially an image of the sun, which I've recreated.
On this,
[INAUDIBLE].
So this is called a imaging system.
Where, essentially, you create a image of, what you are trying to concentrate.
And the limit, for this imaging system.
It turns out to be the maximum,
concentration you can get for, imaging systems.
Turns out to be not, n square by sine square alpha.
But it turns out to be 1/4 of that.
So it turns out to be, 1/4 of that. So.
These imaging systems are not, the
most, efficient systems for, concentrating, sunlight.
So another more generic definition of these, imaging systems.
Is to essentially, think of these, in terms of these, point sources, or A and B.
So, a imaging system will essentially take this point source A.
And, create a image of that
[UNKNOWN],
over here at the receiver.
Similarly, if you give it another source B, it will
create an image of that back of the receiver as well.
But this is not the most optimal thing for doing light travelling.
If you're, grab the light on this receiver,
which has a finite diameter, a more optimal system.
To essentially concentrate this light as this
nonimaging system, where you have this source A.
So all the light
from that source A is collected on this
receiver, but it does not form any dist, any
distinguished image where you can essentially, you know see
you can see an image of this source A.
But you know we are not we are not concerned about creating
an image of the sun when we are designing these concentrated systems.
All we are.
Concerned about escalating all the photons.
So from a perspective
of, of concentrating sunlight, these, non-imaging
systems, optical systems are much better.
Now another question which sometimes bothers me and, you
know, might might bother you, as well, because I think.
You and I think in the same way.
Is that, what are these non-imaging systems?
You know?
I'm generally used to thinking of these
concentrated concentrated as these big mirrors or
this big parabolic curves.
Which, essentially, you know, they take sunlight
and they concentrate onto this focal point.
So those are your typical imaging systems.
So what are these non-imaging systems? So I want to give you some examples of
these non-imaging systems. So shown here is is one such systems,
and it's called a compound Parabolic concentrator, so you can
see how it's it's often abbreviated as CPC, where it's compound.
[NOISE]
And a parabolic you can see that the shape of this is is a
parabolic and it is a concentrator because it's concentrating this light.
So these CPVs, CPC systems you can see that
they essentially form a case of this non-emitting systems so you might have a.
Light coming in and it essentially,
you know, it goes and hits this reflective plate at all kinds of angles.
And this acceptance angle would be essentially given by let's say you have a
ray of light which comes and hits at exactly at this wide grazing angle.
Or maximum limit would be given by this light
which hits it exactly at this angle of 90 degrees.
And you can see that if you make this
light incident at angle which is greater than your
[UNKNOWN],
so let's say that my
[UNKNOWN]
angle was theta.
And I make the sight, incident at an angle higher than that so you can
see that essentially it will come in and it would essentially bounce back.
Or you know this angle would be essentially so that this
is greater than 90 degree or this is essentially on its way.
Out and it essentially goes out of the systems.
So this is one way
to design these non-imaging objects.
And the CPC can in fact come very close to this theoretical limit.
But you can see this is, you know, this parabolic and this
compound this this compound parabolic shape is not the easiest you know.
Which which glass makers or people who make
these mirrors might be most accustomed to making.
So a more easier way, or a more practical way
which many times used to make these Non-Imaging optics is to essentially
take these take this take this imaging optics.
Such as this parabolic parabolic disc or this circular mirror and
then use it to essentially make this light incident not directly on my solar cell.
So let's see my solar cell is located over here.
On my CSP system located over here.
So instead of making the slide directly inside on the sun, what I'll
do that, do now is essentially place this non imaging secondary optical source.
So I place the secondary optical source over
here and many of times it could be another
set of letters or it could be just a prism where this in fact could a, a refractive.
Index of n, which is higher. So I can make the rest of this
system in in air or you know, not using any special material.
But I can place this secondary optics over here.
Which is a glass prism, let's say, with a refractive index of of n.
And this this second resource, it does two things.
So instead of.
So producing
this image, it randomizes this light which is coming in here, and it can take light
from these you know, these off image producing solar cells.
And it essentially creates a non-imaging system, and further if I design it with a
refractive index of n, then my maximum concentration also increases by n square.
So these are few examples that you know, hopefully give you
some idea.
Of how this concentration system are designed.