Chapter 6 :Photometry
PHOTOMETRY
1. INTRODUCTION
Photometry is the branch that deals with the measurement of light (Photo = light, metry = measurement).
Light (by which objects are seen) is either reflected by the object or is emitted by it. Most of the objects are seen by light reflected from them, but objects like electric lamps, stars, sun, etc., are seen by light emitted by them. Now a days, to safeguard against eye strain, standards of illumination have been set up. Therefore in order to achieve the correct illumination it is necessary, not only to measure the quantity of light emitted by a source but also the amount of light falling on the surface. It has been found that the illumination in a classroom should be about 15 lumens per sq. ft. whereas in an operation theatre in a hospital it should be of the order of 300 lumens per sq. ft.
2. STANDARD CANDLE
In early days, the standard candle was taken as, a standard unit of the illuminating power of a source. A standard candle is one, which is made of sperm wax weighing of a pound, inch in diameter and which burns at the rate of 120 grains per hour. The normal height of the wick was being 4.5 cm. If a source gives light 60 times the light given out by a standard candle, its power is taken as 60 candle power. The power of all sources of light is calculated in comparison with a standard candle, But depending upon the conditions i.e., change in the shape of the wick and size of the flame during different seasons, such a standard unit cannot be used for scientific work. It was found that the flame of a candle was not of constant brightness in spite of careful specifications.
With the advent of gee lighting, a need was felt for a more reliable standard. The VernonHarcourt pentane lamp burns pentane vapour and air mixture under specified conditions and gives light of about ten times the original candle. With the progress of science, in the year 1948 an international unit of light was adopted.
The primary standard of light is defined in terms of black body radiation at a definite temperature. A small hole constituting the
Fig 6-1
black body is at the end of cylinder of fused thorium oxide about 4.5 cm long and 0.25 cm internal diameter. It is kept at a constant temperature by being immersed in freezing platinum at a temperature of 17730 oC, in a crucible of thorium oxide (Fig 6-1). Thorium oxide has a higher melting point than platinum.
Platinum is melted by the heat produced by eddy currents induced in it by a coil carrying a high frequency electric current. When allowed to cool platinum remains at if is freezing point for a short time. During this time, the brightness of the hole in the cylinder defines the standard source. Originally the unit of illuminating power of sources (luminous intensity) wee taken as candle power. The unit now used is Candela (It is Latin word for candle) or International Candle. One candle is actually equal to 0.982 times the original candle. International standard candle or candela is defined as 1/60 of the light (luminosity) coming out of a hole 1 sq cm in area in a hollow cavity acting as a black body radiator maintained at the freezing point temperature of platinum (1773oC).
Now a days, the illuminating power of a source of light viz., glow lamps, incandescent lamps, electric bulbs, etc., is given in terms of the above standard unit.
Secondary Standards. As primary standards cannot be used and prepared readily and as they require a lot of technical skill and precision, for practical purposes electric bulbs having tungsten filaments are very carefully compared with primary standards. These electric bulbs having a known value of illuminating power are available and they are worked at the specified current and voltage.
Therefore, in order to find the illuminating power of any source, it is generally compared with these secondary standard electric lamps.
Luminous Flux. The amount of light (i.e., visible radiant energy which flows from a source or illuminating surface in one second is known as luminous flux. (It is only that part of the total radiation, which is visible and can affect the eye.)
Lumen. It is the unit of luminous flux. It is defined as the luminous flux per unit solid angle due to a point source of one international candle power.
Fig. 6-2
Let there be a point source of light of one international candle power. Draw an imaginary sphere of radius r with the source as the centre (Fig. 6.2).
Suppose the total flux = F
Total solid angle = 4 steradians
One lumen =
F = 4 lumens
Therefore, the total flux due to this source . 4 lumens and the total flux due to a source of x candle power = 4 x lumens.
Note. Lumen is also defined as the flow of light energy per second through 1 sq. metre of a surface of one metre radius, when a source of one international candle power is placed at the centre of curvature.
3 INVERSE SQUARE LAW
Consider a point source of light at S. Draw two spheres of radii R1, and R2 (Fig. 6.3). Let the source give out Q units of energy per second.
Consider a surface AB of area = S1 and the surface CD of area = S2
Amount of energy flowing across AB in one second,
Also amount of energy flowing across CD in one second.
As E1 = E2
or (i)
Also energy flowing out of the two spheres per unit area per second is given by
(ii)
The inverse square law Mates that the amount of light energy falling on a given surface from a point source in inversely proportional to the square of the distance between the surface and the source.
The law holds true when the source is a point. It is also true when the size of the source in very small as compared to the distance of the surface from the source.
4.INTENSITY OF ILLUMINATION AND LAMBERT'S LAW
The intensity of illumination is defined as the flux per unit area incident on a given surface, the ray falling perpendicular to the surface.
Consider a point source of light S and an element AB of surface area a that subtends a solid angle w at the point S (Fig. 6.4).
Fig. 6-4
A flux of F lumens falls on the aea AB. Intensity of illumination on AB
= I = F/a
L is the illuminating power or luminous intensity of the source and it is defined as luminous flux per unit solid angle.
Its unit is candela.
Let the area AC be a1.but a1 = a cos
Solid angle
This is known as Lambert’s cosine law, i.e. the intensity of illumination is directly proportional to the cosine of the angle of incidence of light radiation on the given surface.
To conclude, the intensity of illumination is :
(i)Directly proportional to the illuminating power or luminous intensity of the source.
(ii)Directly proportional to the cosine of the angle of incidence.
(iii)Inversely proportional to the square of the distance between the source and the surface.
Special case.
If = 0, i.e., if the angle of incidence is zero, the surface in normal to the incident radiation and cos = 1
5. UNITS OF INTENSITY OF ILLUMINATION
Lux or metre-candle. It is the amount of light falling on a sq metre spherical surface of radius one metre, when a source of one candle power is kept at the centre of the curvature.
Also, one lux = one lumen per square metre.
Phot. It is the unit of intensity of illumination and is equal to one lumen per square cm.
Therefore, it is a bigger unit and is equal to 10000 lux or metre. candle.
Footcandle. It is the unit of intensity of illumination used in England and is defined as the amount of light falling on one square foot area of a spherical surface of radius one foot, when a surface of one candle power is kept at the centre of the curvature. 1 foot-candle is also known as 1 lumen per sq ft.
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Chapter 6 :Photometry
TABLE
Important Values of Illuminance
(Intensity of Illumination)
Method of illumination / Lumens/m2Star Light
M Moon Light
Tube Light
Day light (inside near windows)
Overcast Day
Sun light (Maximum) / 3 X 104
0.2
100
105
104
106
TABLE
Important Values of Luminance
(Illuminating Power)
Light Source / Candles/m2White paper in moon light
Moon’s surface
Clear sky
Candle Flame
Tube Light
White paper in sun light
Standard Source
Tungsten Filament (2700 K)
Sun's Surface / 0.08
2.9 X 103
3.2 X 103
5.0x103
6 X 103
2.5x 104
6.0 X 105
107
2 X 109
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Chapter 6 :Photometry
6. BRIGHTNESS OF A SURFACE AND ILLUATION
The brightness of a surface depends on the reflecting power of the surface and it is not the same as the intensity of illumination. This will be clear from the following examples:
1. The brightness of a white chalk on the blackboard is very high as compared to the black polish on the board but the intensity of illumination on the white chalk and the black polish is the same.
2. If the two opposite walls of a room are painted with white paint and red paint respectively, then the wall with white paint appears brighter. as compared to that with red paint. But the intensity of illumination on both the walls is the same as the amount of luminous flux per sq. cm incident on each surface is the same.
Due to these reasons, the brightness of a surface is defined as the luminous flux per square cm coming out of the surface after reflection from the surface. If I is the intensity of illumination and r is the reflecting power of the surface, then the brightness of the surface = rI.
7. PHOTOMIETER
It is an appliance used to compare the illuminating powers (luminous intensity) of two sources of light. The following types of photometers are in common use:
(1)Rumford photometer (2) Bunsen's greasespot photometer (3) Bouguer's photometer (4) Joly's photometer
(5) LummerBrodhum photometer (6) Flicker photo. meter
(7) Photovoltaic photometer.
In this chapter only the last three types are discussed because the student is already familiar with the former ones.
8. LUMMER AND BRODHUM PHOTOMETER
S1 and S2 are two sources of illuminating powers L1 and L2 respectively. These two lamps S1 and S2 are placed on the opposite side of a white opaque screen (Fig. 6.5) and the diffused reflected light from the two, faces of the screen is incident on the two identical prisms P1, and P2. The light after reflection from these prisms pause through the LummerBrodhum, cube AB.
The LummerBrodhum cube consists of two right angled isosceles prisms A and B in contact with each other. The edges of the prism A are cut in such a way that a film of air exists between the two surfaces of contact. It will be seen that light rays are totally internally reflected at all the points in the two prisms except at the centre. Thus in the field of view of the telescope it is observed that either (i) the inner portion is dark as compared to the outer or (ii) the outer portion is dark as compared to the inner portion fig. (6-6). For balancing, the distance of one source in fixed and the distance of the other is adjusted such that the field of view is equally bright.
Fig. 6-5 Fig. 66
When the field of view is equally bright, ”Photometric balance” is said to have been obtained.
Theory. After the photometric balance has been obtained, let the distance of the source S1 from the screen be R1 and the distance of the source S2 from the screen be R2 (Fig. 6-7).
Fig. 6-7
and
Here
and
If r1 in the reflecting power of the surface F1 and r2 is the reflecting power of the surface F2 then;
brightness of the surface (i)
and brightness of the surface (ii)
After the photometric balance, (i) and (ii) are equal
If r1 = r2, i.e., the two faces of the screen have the same reflecting power , then;
Hence (iii)
Note. This photometer cannot be used when the two sources emit light radiations of different wavelengths (colours).
9 F1LICKER PHOTOMETER
When the sources emit light radiation of different wave lengths, the flicker photometer is used. In this case, A is a plaster of paris disc out into sectors and B in a white diffusing surface. Light from a source S1 is reflected by the surface A while that of S is reflected by the surface B (Fig. 6-8). A is rotated about a horizontal axis while it is always inclined at an angle of 45o to BE. Light from the surface A and the surface B after reflection is seen through the microscope M.
The disc A is rotated and it is observed that flickering occurs in the beginning. The distance of the source S1 from the disc A is adjusted so that no flickering in observed. Suppose the distance of S1 from the disc A is R1. Now replace the source S1 by the second source S2 keeping S fixed at it is original position. Adjust the distance of the source S2 from the disc A sothat no flickering of light is observed in this case also. Suppose the source S2is at a distance R2 from the disc A.
Fig. (6-8)
It is observed that no flickering is produced even when the sources are of different colours. If L1is the illuminating power of the source S1 and L2the illuminating power of S2 then,
10. PHOTO VOLTAIC PHOTOMETER
A photo voltaic cell consists of a copper plate and a layer of cuprous oxide is formed by oxidising one side of the copper plate.
If the cuprous oxide surface is exposed to light, it emits electrons. The number of photoelectrons emitted depends upon the intensity of the incident radiation. This phenomenon is known as photoelectric effect.
Fig. 6-9
A photo voltaic cell (barrier layer type) can also be used in a photo voltaic photometer. it consists of an iron plate on which there is a layer a selenium. Selenium is coated with a very thin layer of gold or platinum through which light can penetrate to the selenium layer (Fig. 6.10).
Fig. 6-10
1.Comparison of illuminating powers.
The source S1 is placed at a certain distance R1 from the gold layer of the cell. Photoelectrons are ejected, and the current flows in the galvanometer (Fig. 6.9). Let the deflection in the galvanometer be .
Replace the source S1 by the source S2 and adjust its distance from the cell so that the same deflection is produced in the galvanometer as in the first case. If the distance of the source S2 from the cell is R2
then,
If L1 is known, L2can be calculated.
2. Verification of inverse square law.
A source is placed at different distances from the photovoltaic cell and the corresponding deflections in the galvanometer are noted. The deflection in the galvanometer is directly proportional to the intensity of the incident radiations.
I
If R is the distance of the source from the cell , then
The value R2 will be a constant.
If a graph is plotted between and 1/R2 it will be a straight line (Fig.6-11). This verifies inverse square law.
Fig. (6-11)
11. DETRMINATION OF THE REFLECTING POWER OF MIRRORS.
The reflecting power of mirrors can be determine with the help of Lammer-Brodhum and Bunsen photometers. A source S is placed at a distance R from the screen and another source S1 is placed at such a suitable distance from the screen so that the photometeric balance is obtained Fig (6-12).
Fig. 6-12
Suppose the distance of the source S1 from the screen is R1 . If L and L1 are the illuminating powers of the sources S and S1 ; then,
(i)
Now the mirror M is inclined at an angle of 450 to the line joining AB and the source S is brought to a point A' as shown in Fig. 6.12 (ii).
By moving M and the source S together, a position is found where photometric balance is obtained. Suppose in this position, the distance of the mirror from the Screen = a and the distance of the source S from M = b.
If r is the reflecting power of the mirror, then in this case L' = rL i.e., light reflected from M can be considered to he due to a source of reduced illuminating power L'
or
(ii)
From equations (i) and (ii)
As a, b and R are all measurable quantities r can be calculated.
12. DETERMNATION OF TRANSMIMON COEFFICIENT
A source S is placed on one side of a screen at a distance R from it and another source S1 is placed at a distance R1 from the screen on the other side so that the photometric balance is obtained (Fig. 6-13).
Fig.( 6-13)
(i)
Now interpose the transmitting plate P, between the point A and the screen. Place the source S1 at a suitable distance from the screen so that the photometric balance in obtained.
Suppose, in this case, the distance of the source S1 from the screen is R2. If the luminous flux on, the screen in now due to the effective illuminating power L', then L' = t L1were t isthe transmission coefficient.
(ii)
From, equations (i) and (ii)
Example 6.1 A small source of 100 candlepower is suspended 6 m vertically above a paint P on a horizontal surface. Calculate the illumination at a point Q on the surface 8 m from P and also at P.
Solution:
The illumination at a point = according to Lambert’s law (Fig6.13)
Fig. 6-13
illumination at
Since = 0
Cos = 1
Ip = 100/(6)2 = 2.77 Lumens/sq.m
Ilumination at Q =
Here, R = SQ = = 10 m
Also, cos = 6/10
= 0.6 lumen / sq .m
Example.62. A photo voltaic cell is used to compare the illuminating powers of two electric lamps. A full scale deflection is obtained in the galvanometer connected to the cell when a lamp of 16 candela is placed 100 cm from the cell. Calculate the illuminating power of the other lamp, which must be placed at a distance of 150 cm from the cell to obtain the same reading in the galvanometer.
Let the illuminating power of the first source = L1= 16 C.P.
distance of the first source from the cell = R1= 100 cm
Illuminating power of the second source = L2 = ?
Distance of the second source from the cell = R2 = 150 cm
For photoelectric balance
= 225 C.P.
The illuminating power of the second source is 225 candle power or candela.
Example 6.3. A lamp is situated 10 cm in front of a plane mirror. A screen placed at a distance of 30 cm from the mirror. The light after reflection produces the same illumination on the screen as a lamp equal in every respect to the first lamp but situated 70 cm from the screen (given that the first lamp does not give direct light to the screen). Find the reflecting power of the mirror.
Let r be the reflecting power.
a = 30 cm
b = 10 cm
a + b = 30 + 10 = 40 cm
r = 70 cm
= 0.326