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Welcome to this lecturer 5, laws of illumination. In the previous lectures we had seen the need
for illumination and subsequently we saw how the natural radiation is spread and based
on that we look to have the artificial illumination systems as close to the natural illumination
as far as possible. And why are we doing all these? We are doing all these because 80%
of our information acquisition is through our eyes, the most important sense and depends
on the illumination levels and therefore the next two lectures had concentrated on the
functioning of the eye. As it goes, in any face sphere of science and engineering it
is necessary that we are able to quantify the things which we study. And we also know
that the physical processes follow certain observed relationships which we call them
as laws and hence the title of this lecture has been titled as laws of illumination. Before
we proceed further we look at the objectives of this lesson that is to say that at the
end of this lesson, one should be able to define what is the standard of illumination.
As already brought out to you quantification is a very important thing. It is not enough
if I say that I have more light or less light, I should be able to give a value or hang a
number to it to say that this is better than that and that's possible by way of standardization.
And the way light is felt on the objects follows certain laws and that's what we going are
to address. The second objective is listed as what is a candela. As we go along, we will
know what is a candela. In fact incidentally candela is the standard way of assigning a
light output and as may be understood, it is a variation of the term candle. All of
us familiar with candle, whenever there is power cut these days of course we have emergency
lamps but early days we used to use candles. And then there is a term called MSLI which
stands for mean spherical luminous intensity and one needs to understand that. And as already
told as title, the lecture title has laws, the one of the first laws that is associated
with this luminous principle is Frechner's laws. So, one should be able to state the
Frechner's law at the end of this lecture. And as has been with many physical phenomena,
there is always an inverse square law associated. Recall the mechanics we have an inverse square
law, recall electrostatic we have inverse square law. So it is interesting that most
physical phenomena have the inverse square law governing the energy, delivery and utilization.
So, let's look at the laws of illumination and as I said before, we really going to laws
of illumination, it becomes necessary for us to know how we are going to standardize
the light output. And that is to say we are going to hang some numbers to the light and
how do you do that? Because the first source of artificial light has been a candle. The
first standard that has been adapted for light output has been a wax candle, however it is
highly unreliable. Recall that in any meteorology or measurement technology, the standard adapted
must be stable, must be reproducible from one laboratory to the other laboratory, hence
it was considered to be very unreliable which was subsequently replaced by what's known
as vaporized Pentane lamp.
A Pentane lamp running on the pentane vapor that is why it is called vaporized pentane
lamp which emitted light approximately 10 times the original wax candle. This was subsequently
taken which was subsequently in the year 1909, it was replaced by incandescent lamp and it
is compared with a Pentane lamp. However this has not been used much because as already
told, it should be reproducible which is not easily possible with the incandescent lamp,
hence there was a move to look for a better standard.
And probably in the year 1948, there was a better standard adapted and as written out
here it was based on the light output from what is called as a radiator. Recall in an
earlier class when we are talking about the physical processes involved in artificial
light, we talked about various light output devices like black body, gray body, selective
radiator, etc. So here we have standardized by considering a good radiator, radiating
light through a small aperture and the platinum is been maintained at it's what do you call
solidification temperature and that is being adapted as the standard.
What are the components of this standard? These components of this standard are as can
be seen, number one the radiator which is essentially fused thoria other words thorium
oxide which is about 45 mm long with the internal diameter 2.5 mm. So this aperture is packed
with fuse thoria at the bottom. This is supported obviously it is a powder packed, so it has
to be put in a container. It was put in a container consisting of a fuse thoria crucible
which had a 1.5 mm aperture and all these had to be kept in a good thermally insulted
environment. And this is possible by keeping it in a large refractory container and the
platinum, the pure platinum that is used is melted and it is to be maintained at what
temperature? It is at the freezing or solidification temperature which is 1773 degree Kelvin. And
to do that, the high frequency Eddy currents are adapted and it is observed that this gives
rise to approximately 589000 candles output, light output spread over a units surface area.
And therefore it was believed okay, though initially it was of this kind, it was later
standardized as the light corresponding to 600000 units of original thing.
Let's have a look at the picture of the standard. As can be seen this is the primary
standard of light. As you can see there is an opening from where the radiant output is
brought out, this has got an opening of about 1.5 mm in diameter and there is a cubical
which is fused thoria cubical kept in a highly refractory environment. As we said it has
to be thermally insulated, so it's got an outer this thing consisting of unfused thoria
in which in this cubical as already told, the radiator is pure platinum which is vertically
supported. The crucible had a dimension of approximately 45 mm in length, vertical length
and 2.5 mm diameter and this platinum is maintained in a molten state. That is at the solidification
or freezing temperature of platinum that is 1773 degree Kelvin.
Now, this having been adapted, we said this gives out an output which was closed to 589000
candles per meter square which is been made equal to about 600000 units. So having said
that the primary standard of light is this but today we adapt the light to be this and
any light radiation output we compare has to be with respect to this. Having said this,
we redefine our candela or what we said as the light output due to an original wax candle
is the luminous intensity in the perpendicular direction.
Obviously when we talk about the light output, we look at the ability of human eye to perceive
the object when light falls in that. So we and this calls for the normal radiant, radiation
to be considered, hence we talk in terms of luminous intensity in the perpendicular direction
which is 1 by 600000. Recall we said the primary standard corresponds to about 600000 units
of original candles, therefore candela has been defined as 1 over 600,000 of a black
body which is nothing but here with platinum, pure platinum maintained at solidification
or freezing temperature of platinum under what conditions. The standard atmospheric
pressure. The candela is abbreviated as cd okay that means the candles or candela gives
us an idea of luminous intensity or light flux radiating capacity of a source of lamp
that is what it is.
Now we go further try to express the effect of the light flux on the objects. Now how
do we consider an electric system? We have a charge; we talk in terms of the field by
talking at any point, the effect of this charge on a unit positive charge. The similar way
one could define the light in luminous intensity at any surface. In order to understand this
let us consider a transparent sphere at the center of which we place which is marked o,
place a light source which produces one candela and consider on this transparent sphere which
is, whose radius is one meter, consider a solid angle of 1 steradian. If we consider
a solid angle of 1 steradian, it encompasses an area of 1 meter square only transparent
surface. The normal light output during, due to this would be standardized as the basic
unit of what we call luminous intensity and is defined or by definition we call it as
one lumen.
Let us look at it once again, what did we do? We considered a transparent sphere of
1 meter in radius. We took a standard source whose light output is 1 candela placed at
the center of this sphere O and then consider the light radiating out of this over a surface
area or on the surface subtended by a 1 steradian solid angle. By the definition of solid angle,
we know the radius is 1 meter and the solid angle is 1 steradian, the area and compassing
surface which is marked here would be 1 meter square then the normal light output through
this 1 meter square is termed as 1 lumen and this is the unit of a luminous intensity,
just as the effect of electric charges is felt in terms of the force exerted by those
charges on test charges at any point and the normal direction.
Similarly the light flux coming out of this source is felt in to the luminous intensity
and it is standardized or its unit is by definition, the luminous intensity over 1 steradian by
a 1 candela source on this surface of a 1 meter sphere is termed as 1 lumen. In that
sense the total flux that's coming out of the source, considering a source placed in
all directions about the source because if we consider all directions we can think of
a spherical surface. And the total solid angle subtended would be 4 pi and recall we considered
a sphere of 1 meter radius in that case total area would be 4 pi and therefore it is said
that if we place a 1 candela at this center of sphere of 1 meter radius, we would get
a flux of 4 pi lumens, that is the thing.
So how do we go about understanding this? We have defined the basic unit of luminous
intensity which is nothing but 1 steradian, the flux coming out of 1 steradian by a 1
candle source placed at the center of 1 meter sphere is termed to be 1 lumen. And therefore
total flux due to 1 candela placed at the center would be 4 pi lumens. As against this,
if I take a source which has I candela, I is normally used to denote certain candle
power of a source, this is also called candle power. See it is very simple recalling that
the first and fore most artificial source has been wax candle that's how we have got.
Let's see how we go about doing this.
Let us consider the solid angle subtended over a certain area is D omega and then the
total luminous intensity is I candela that is the source candela power is I candela,
luminous flux in D omega, if we call it that is over the solid angle D omega is termed
d phi then we have that as I into D omega lumens. Recall 1 candela over 1 steradian
produced 1 lumen. If I have I candela over a range of D omega solid angle, it will be
I D omega lumens. And therefore I say that D phi by D omega would be my I, the candle
power.
Now there is another term which we often use with respect to these lamps because now recall
after we started using electric lamps using thermo effect thermo luminance, it's been
the incandescent lamps which are nothing but a filament maintained at a temperature placed
at the center of a class envelope which means it had the ability of radiating light in all
directions. So in a sense it could be viewed as a source of light, a point's source light,
so it had the ability of radiating light in all 4 directions. It means the overall solid
angle subtended by the light output is 4 pi and therefore the term means spherical luminous
intensity is talked of, means spherical luminous intensity it means luminous intensity when
considered in all directions. For a point source you will find that it is same equally
distributed in all directions. When we go on to the control of gear, we can observe
depending on the application one could orient the amount of light flux radiated in different
regions to be varied and that's where it becomes somewhat important.
Now having said luminous intensity and the luminous flux, now how do we know how much
light is really falling an object and we have to consider the area of the object into consideration.
And this is defined by yet another term in fact that is what we call as illuminance.
See we have not yet come to loss of illumination; we are in the process of standardizing the
light output, we have learnt what is a primary standard. Now we have also learnt how luminous
flux is defined and so we say the power, radiating power of lamp is expressed in terms of the
primary standard and is talked in terms of candela and the amount of light that is coming
in a particular zone is talked in terms of the luminous flux which is lumens and this
luminous flux per unit area is what is termed as a illuminance.
It's very important because as you go along designing the illumination systems, you will
find that we talk in terms of recommended illuminance levels for various applications.
That is a very important issue. We talk in terms of lumens per square meter and this
is categorized or standardized as lux 1 lumen per meter square is a lux. So illuminance
if you consider, again observe the diagram shows at the center of a sphere we trying
to get illuminance at any point on the sphere. So assumption again here is that the source
of light is a point source. Let's say it has the candle power of 1 cd then the total
flux considering the radiant in all 4 directions or all directions in the spherically would
be 4 pi. Remember the area of this sphere is 4 pi r square and hence the illuminance
would be 4 pi by 4 pi r square or 1 by r square lux. So illuminance radially away due to a
point source at a distance r can therefore be talked in terms of.
So observe the figure here we are looking at a particular source deemed to be a point
source marked s placed at a point P and has the candle power or luminous intensity of
I candela distant from a plane of observation at d units. Then on the illuminance in the
surface by definition is I by D squared lux. Now in trying to find illuminance, we are
looking at the normal, normal light flux incident. It is quite possible that there is every chance
of light coming in an oblique direction. So some of these issues have to be addressed
by way of considering how this is governed but it's time we took at the first of these
Laws which we call Frechner's Law.
This is based on an observation made by Weber in 1830. This is about the way human sense
organs respond. Consider a stimulus of intensity I and let it be having a least perceptible
increment that can effect the sense organs as dI. The observation made by Weber says
that ratio dI to I is a constant. This is under the situation, remember talking of the
way I functions we said there are certain consideration the way I functions, fatigue
is one important things. So this observation says that it holds good under fixed fatigue
attention and expectation. See there are two things, the eye perceive is the physical device
thorough which you allow the light or the information to get in to it but it is the
brain that processes and you are able to see that means there is some amount of expectation.
Often it is said you read what you want to read more than what is written unless it is
properly written. So what is the Weber's observation say? It says if there is a certain
stimulus I and it has a least perceptible increment dI that can affect the sense organ,
the ratio of DI to I is a constant.
This is further examined by the Frechner's with respect to your illumination and he has
found that there is a logarithmic dependence as far as optic nerves go and that is expressed
as S sensation produced by optic nerve has. So what do you have, S equal C log I by I0.
What this I0? I0 is the threshold that is the minimum of luminance intensity that is
able to produce any this thing on your eyes. So there are, this aspect has to be kept in
mind that while designing light sources because any change how it is going to affect our human
eye is depended on this Frechner's Law. The next thing as I said the inverse square
law just as in any other physical system we have, this in fact is very apparent even from
the varied definition of a illumination, illuminance.
We said the illuminance at any point due to a point source turned out to be the ratio
of luminous intensity to the square of distance between the point and the thing. So we find,
so this is what is expressed in this equation. I am afraid that in this equation 3, it should
be IX is equal to K by dX square not K dX square, to that extent there should be a correction
where dX square is the distance. Now talking of the illuminance, we consider these light
coming in the normal direction from a point source when defining the illuminance or considering
the inverse square law in it' basic form but we did mention that it is quite possible
that the light from the source may not be radiant on the object, incident on the object
in the normal direction, it could be obliquely designed.
How do we go about taking care of illuminance and those conditions? Illuminance however
defined in terms of the normal light output and therefore this is by definition obtained
from what we call Lambert's Cosine Law. So how many laws we have seen? We have seen
there are three basic laws, the first law says that the ratio of luminous intensity,
two the perceptible change in the luminous intensity is a constant and this sensation
with respect to the human eyes is logarithmic in nature that is a very important issue.
So you cannot keep on increasing the illuminance, light output luminous flux and at expect your
eyes to up get better and better. So since its logarithmic the marginal increase may
be enough beyond that unless you try to have more uniform flux radiant, you cannot get
any improvement in the observational characteristics. Second one is actually direct corollary of
the definition of illuminance which says illuminance is inversely propositional to the square of
the distance. This becomes more clearer.
Now here in this picture what is it we are trying to see? You observe that there are
3 planes, 2 planes, one is source plane marked S, it could be an array of lamps which are
radiating light in the normal direction shown by a thick arrows pointing from S towards
right. The normal plane with the object plane, object plane is inclined at an angle alpha
in fact we said mentioned about Lambert's cosine law, this alpha in the cosine law comes
from this angle between the normal plane and the plane of the object. When we write I cos
alpha, what is it we are doing? We are essentially taking the total light flux incident on the
normal plane. So that is what it is, you can see that it is at an angle alpha, bb is the
axis passing through the object plane on which the light is incident and you are trying to
observe.
So it says I itself on that is proposal to I cos alpha that's obviously you can resolve
the light into the normal component and the horizontal I mean the horizontal components.
Now let us extend this and try to analyze for various situations in fact incidentally
this law is also called as a law of emission. Now this picture out here shows this is a
typically scenario, you find a lamp placed or a source placed at point A and the line
bc is essentially a line on the floor let us say, this can be viewed as a the typical
room with the light hanging from the ceiling suspended at a height b from the floor. So
if you go by the definition of illuminance, one could work out illuminance at varying
point on the floor and how it varies, okay. So this can be, this is in fact applying the
definition of illuminance. The definition of illuminance is what? It says if the candle
power of source is I then illuminance at the point of interest is I over the distance square.
Let's say we look at a point right below the lamp that's where you have I over b
square which means it's got the maximum normal illuminance. Now observe when we move
to the point C, the radially outward light rays are inclined to the normal axis and therefore
normal light flux would no longer be I but it will be I cos theta, theta is the angle
subtended by the radial output in the source and the normal axis to the point of the observation.
And what is a distance? Distance is d. So we find that recall this angle can go from
theta equal to 0 to 90 at the most. You recall if the point of observation is B right below
the lamp what is theta? Theta is 0 in that case because the radial output light ray and
the normal axis are co-incident theta is 0 where as when you go along away from the lamp
farther and farther you are going to get theta higher and higher. And we know that when you
move from 0 to 90 degrees, cos theta goes from 1 to 0, it reduces from 1 to 0 and that
been the case you have a decrease in your eye normal light flux as you go away and luminance
is depended on the distance between the source and the point of observation. As can be seen
very clearly at the point B you have the minimum distance hence and you have the maximum light
flux, normal light flux which means you have maximum illuminance right below the lamp.
Going by this we can draw the illuminance as a function of your d by, it should have
been d by b, it's not d by n and it is marked over a distance of what you call from 0 to
3.
If you observe carefully, initially for some small distance it is near about the maximum,
this can be the curve pertaining to your luminous intensity or illuminance. And as can be seen
it's nearly same as under the lamp only for short distance that is you can allow or
have nearly same amount of illuminance or light flux only over an angle of 60 to 75
degrees from the vertical. That is this theta which you are observing beyond that it would
give very large depreciation, it could be ineffective and this aspect has to be borne
in mind in trying to have uniform illuminations. It is obvious supposing I am working on a
cable which is typically 1 meter by half a meter, I would like to have as nearly as possible
same illumination level all through and that is the issue. And the single lamp may not
serve to have completely uniform illuminations and therefore you one may have to go in for
more than one lamp.
We will also see that as against the points source a line source, line source recall the
florescent lamps or tube lights which we use are nothing but line sources of light and
just as we found that light flux is inversely proportion to the square of distance for a
point source. We can see a similar direction that due to the line source would be inversely
proportional to the distance as against square here and if you are able to have a large sheet
of light, it could be independent of that distance. So these are some of the things
we will revisit as we go long. So now going back to the thing. We take this example, we
try to express illuminance along the distance away from the point below the lamp. As can
be seen this is how the illuminance is going to vary that is very important we said this
source that in our trying to have the systems, we should keep in mind this angle theta between
the radial light ray and the normal to the plane should not be more than 60 degrees to
the vertical.
Illuminance at the B therefore is luminous intensity or the candle power or candela in
direction AB. Recall the diagram, we had a lamp located at the point A and right below
we are talking about the point b is right below the lamp and the height between this
point and the height of this source above the floor is B units and therefore it is luminous
intensity direction AB by B square. Whereas, what should be the illuminance at C? It should
be luminous intensity in direction AC by AC square and which is luminous intensity in
direction AB into cos theta by what is AC square is b square plus d square. And you
find that the luminous intensity at, in terms of your AB one could... So you find this is
how it can be expressed and this rate, this is how one has been able to draw this curve
with respect to distance observed that in this relationship you could, you can bring
this b and this is how one does.
Remembering cos theta is B by, so what do we get? We get that illuminance at C is nothing
but illuminance at B into cos q theta or expressed in other words is 1 plus d by b square cubed.
So this is how and all this says that illuminance is a maximum right under the lamp and it keeps
on decreasing and the variations is going to be this nature and should be, it is best
used only when it is kept that the theta within 60 to 75 degrees. Now having said so much
about the way to standardize the light output, we said it is in terms of luminous intensity
which is unit of which is a candela which is based on the wax candle later adapted as
the platinum or a radiator maintained at melting or freezing point of the platinum in a thoria
crucible which has adapted as a standard primary standard which is equal to how much? 600000
candelas, light output due to that is 600000.
Now if that be the luminous intensity then we define the luminous flux as categorized
in terms of lumens and for a point source, we say it emits light in all directions uniformly.
And therefore we talking in terms of a what we call mean spherical luminous intensity
and total light flux is in all directions, therefore subtends over 4 pi steradians of
solid angle and hence is termed in terms of 4 pi I and it is where I is the candle power
and is termed in terms of the lumens. Now once you have the luminous intensity and luminance,
the effect of this on the plane of the observation is talked in terms of a illuminance which
is luminous flux per unit area is talked in terms of lumens per meter square or lux.
Now all these is governed by set of laws which we call them laws of illuminance, illumination.
First law is that due to Freshener which tells the behavior of I based on the least perceptible
stimulus that affects our sense organs and which was initially observed by Weber or in
biological systems later they can observed by Freshener for optical systems. The sensation
of the optic nerves is logarithmically depended that means increase in light beyond certain
level would not really make much a difference put in other words. The second law, the law,
inverse square law which is a direct outcome of definition illuminance which says it is
1 over x square where x is the distance i over x square and this applied to any arbitrary
plane is taken care by Lambert's cosine law of emission. So having said this, the
immediate requirement would be to access any of the systems that we have and the measurements
or assessments test methods are in fact called as photometry.
And this invariably would have a employing, what is called as photometric bench on which
the on one side the standard lamp is placed I s of I candela. This could be an incandescent
lamp which is compared with the primary standard which is nothing but a perfect radiator maintained
at the temperature of freezing or solidification of platinum and Ix corresponds to the, what
you call the test lamp. What we find is the square screen, this is the dark screen placed
at the center and which can be made to move and it is essentially balanced obtain same
level of illumination on either side from this lamp or that lamp, normally incident
on the screen from the balanced this distances one could obtain the value of I.
So this we will look at in detail. That means what we're trying to do? We move this central
screen till such time the illuminance on either side is same. Illuminance recall is nothing
but luminous intensity by the distance square, so you have Is by d s square is equal to Ix
by dx square. So this becomes the important and in fact more details of these photometric
methods could be covered in a subsequent lecture.
Coming to the summary of the lecture, we have defined the basic unit of light flux as luminous
intensity is a candela which is the intensity of a surface which is 1 by 600000th of a black
body at the freezing temperature of the platinum which is 1773 degree Centigrade under standard
atmospheric pressure.
The luminous intensity over one steradian solid angle by a source of one candela has
been termed as the unit of flux which is one lumen means MSLI is used with all points sources
is the average intensity into solid angle which is mean spherical luminous intensity
in all directions. Luminous flux is luminous intensity in to the solid angle, illuminance
is the luminous flux per unit area.
And the Frechner's law gives us the idea of the response of the eyes which says same
percentage in stimulus from the least amount perceptible gives the same change in sensation.
Inverse square law is nothing but the definition of illuminance which says illumination varies
as a square of the distance inversely.
Lamberts Cosine law of incidence is useful in estimating. Here E is the luminous intensity
at arbitrary point in arbitrary direction which is I cos alpha by D square. This is
cosine Law of emission talks about candle power, incidence talks about the luminous
intensity illuminance that is the lux.
Some of the questions that can be addressed from this lecture are what is the standard
unit of luminous intensity, what is MSLI, what is the standard procedure to measure
luminosity.
Some answers to the previous lectures questions: Quantity as quality of illumination are important,
why? At present eye tasks are more and for longer duration and hence increase illumination,
illuminance is required. So illumination also affects psychology hence quality is important.
What should be the minimum brightness of the surrounding? Brightness of surrounding must
be less than that of the object and should not be less than 0.01 foot lamberts. What
are the three primary colors? As already known they are red, green and blue.
How does aging leads to loss of vision? As can be said aging leads to decrease in adjustment
capability of the focal length of the eye thus higher illumination is required for older
people.
What is chromatic aberration and why it occurs? It is the reduction in acuity due to combination
of different colors. It occurs due to the fact that the eye lens has different refractive
power for different wavelength of light. Thank you.