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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

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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 Vernon-Harcourt 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

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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

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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.)

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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.

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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.

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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.

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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

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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.

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(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.

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Foot-candle. 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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TABLE

Important Values of Illuminance

(Intensity of Illumination)

Method of illumination Lumens/m2

Star Light

M Moon Light

Tube Light

Day light (inside near windows)

Overcast Day

Sun light (Maximum)

3 X 10-4

0.2

100

105

104

106

TABLE

Important Values of Luminance

(Illuminating Power)

Light Source Candles/m2

White paper in moon lightMoon’s surfaceClear skyCandle FlameTube LightWhite paper in sun lightStandard SourceTungsten Filament (2700 K)Sun's Surface

0.082.9 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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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 inten-

sity 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.

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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

grease-spot photometer (3) Bouguer's photometer (4)

Joly's photometer

(5) Lummer-Brodhum photometer (6) Flicker photo. meter

(7) Photo-voltaic 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 Lummer - Brodhum, cube AB.

The Lummer-Brodhum 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

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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. 6-6

When the field of view is equally bright, ”Photometric balance” is

said to have been obtained.

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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 s ource 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

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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

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source S2 keeping S fixed at it is original position. Adjust the

distance of the source S2 from the disc A so that no flickering of

light is observed in this case also. Suppose the source S2 is 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 L1 is the illuminating power of

the source S1 and L2 the 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.

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If the cuprous oxide surface is exposed to light, it emits

electrons. The number of photo-electrons emitted depends upon

the intensity of the incident radiation. This phenomenon is known

as photo-electric 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

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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 gal-

vanometer 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, L2 can be calculated.

2. Verification of inverse square law.

A source is placed at different distances from the

photo-voltaic 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

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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).

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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

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(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.

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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 L1 were t is the

transmission coefficient.

(ii)

From, equations (i) and (ii)

Example 6.1 A small source of 100 candle-power 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

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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.6-2. 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.

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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.

2R)ba(

r

a = 30 cm

b = 10 cm

a + b = 30 + 10 = 40 cm

r = 70 cm

= 0.326

Hence, the reflecting power of the mirror 32.6%

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EXERCISES1. Define lumen, luminous intensity of a source and illumination

of a source. Describe a photometer and explain how it may be

used to compare the illuminating powers (luminous intensities)

of two lamps.

2. Define illumination at a point on a surface. In what unit is it

commonly expressed?

A source of 200 C.P. is suspended 3 m vertically above a point P

on horizontal surface. Calculate the illumination at (i) the

point P and (ii) at a point Q, 4 m from P.

3. Describe the Lummer - Brodhum photometer. How will you

find the reflecting power of a mirror ?

4. Give the working and the theory of comparing the illuminating

powers of two sources of light of different colours. What is the

name of this photometer ?

5. What is a photo-voltaic photometer? How would you verify the

inverse square law with this photometer?

6. Explain Lambert's law.

A lamp of 500 C.P. is suspended 60 m above the ground. Find

the illumination (i) at a point P vertically below the lamp and

(ii) at a point Q, 80 m from P.

7. Describe a photo-voltaic photometer to compare the

illuminating powers of two sources.

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8. A photo-voltaic photometer is used to compare the illuminating

powers of two electric lamps. A full scale deflection is obtained

in a galvanometer connected to the photo-voltaic cell when a

source of 20 candela is placed at a distance of 100 cm from it.

Calculate the illuminating power of the source, which must be

placed at a distance of 80 cm from the cell, to obtain the same

deflection in the galvanometer.

9. A lamp is situated 20 cm in front of a plane mirror. A screen

has to be placed at a distance of 50 cm from the mirror in order

that the light after reflection produces the same illumination on

the screen as a lamp equal in every respect to the first lamp but

situated 100 cm from the screen. Given that the first lamp does

not give direct light to the screen, find the reflecting power of

the mirror.

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