32Photometry

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PHOTOMETRY
▢ Introduction:
❖ Definition: Photometry deals with study and measurement of light energy
❖ Instrument: Photometer
❖ Photometer Use: Used to compare illumination power of different light sources
▢ Radiant Flux:
❖ Symbol: \(R\)
❖ Definition: Total energy radiated by a source per second

Table 1: Radiant Flux

Quantity
Value
Symbol
\(R\)
Unit
Watt
Meaning of watt
Energy/second
▢ Luminous Flux:
❖ Symbol: \(\phi\)
❖ Definition: Total visible energy emitted per second by a source

Table 1: Luminous Flux

Quantity
Formula / Unit
Symbol
\(\phi\)
Unit
Lumen
Relation
\(1\ lumen=\frac{1}{685}\ watt\)
For sphere
\(\phi=4\pi L\)
▢ Luminous Efficiency:
❖ Symbol: \(\eta\)
❖ Definition: Ratio of luminous flux to radiant flux

Table 1: Luminous Efficiency

Quantity
Value / Formula
Formula
\(\eta=\frac{\phi}{R}\)
Unit
Lumen/Watt
Dimension
Dimensionless
Nature
Dimensionless but not unitless
100% luminous efficiency
685 lumen/watt
▢ Solid Angle:
❖ Symbol: \(\omega\)
❖ Definition: Three-dimensional angle used to measure divergence of luminous flux

Table 1: Solid Angle

Quantity
Formula / Unit
Formula
\(\omega=\frac{Normal\ area}{distance^2}\)
For sphere
\(\omega=\frac{4\pi r^2}{r^2}=4\pi\)
Unit
Steradian
Dimension
Dimensionless
▢ Luminous Intensity:
❖ Symbol: \(L\)
❖ Definition: Luminous flux per unit solid angle

Table 1: Luminous Intensity

Quantity
Formula / Unit
Formula
\(L=\frac{\phi}{\omega}\)
For sphere
\(L=\frac{\phi}{4\pi}\)
Unit
Lumen/Steradian
SI unit
Candela \((Cd)\)
▢ Illuminance:
❖ Also Called: Intensity of illumination
❖ Symbol: \(I\)
❖ Definition: Luminous flux incident per unit area

Table 1: Illuminance Formulae

Condition
Formula
Basic
\(I=\frac{\phi}{A}\)
Using luminous intensity
\(I=\frac{\omega L}{A}\)
For spherical distribution
\(I=\frac{4\pi L}{4\pi r^2}\)
Normal incidence
\(I=\frac{L}{r^2}\)
Oblique incidence
\(I=\frac{L\cos\theta}{r^2}\)

Table 2: Laws of Illuminance

Law
Formula / Meaning
Inverse square law
\(I\propto\frac{1}{r^2}\)
Lambert's cosine law
\(I\propto\cos\theta\)

Table 3: Illuminance Units

System
Unit
SI
Lumen/m² or Lux
CGS
Phot
Conversion
\(1\ phot=10^4\ lux\)
Also
\(1\ phot=1\ lumen/cm^2\)
❖ Symbols:
  • •
    \(r\) = distance between source and illuminated point
  • •
    \(\theta\) = angle between incident ray and normal to surface
▢ Principle of Photometry:
❖ Condition: Two sources equally illuminate a screen

Table 1: Photometer Principle

Step
Formula
Equal illumination
\(I_1=I_2\)
Using inverse square law
\(\frac{L_1}{r_1^2}=\frac{L_2}{r_2^2}\)
Final relation
\(\frac{L_1}{L_2}=\left(\frac{r_1}{r_2}\right)^2\)
❖ Meaning: Illuminating powers are proportional to squares of distances from equally illuminated screen
▢ Plane of Illuminance:

Table 1: Illuminance on a Plane Surface

Formula
Expression
General oblique form
\(I=\frac{L\cos\theta}{r^2}\)
Using height
\(I=\frac{Lh}{r^3}\)
Using angle and height
\(I=\frac{L\cos^3\theta}{h^2}\)
❖ Symbols:
  • •
    \(h\) = perpendicular height of source above plane
  • •
    \(r\) = distance from source to point on plane
  • •
    \(\theta\) = angle between incident ray and normal
▢ Important Relations for Problems:

Table 1: Problem-Solving Formulae

Condition
Formula
Total luminous energy falling on surface
\(Q=IAt\)
Box-type camera exposure time
\(t\propto\left(\frac{f}{d}\right)^2\)
Equally satisfactory photographic prints
\(It=constant\)
Two photographic cases
\(I_1t_1=I_2t_2\)
Using source intensity and distance
\(\frac{L_1}{r_1^2}t_1=\frac{L_2}{r_2^2}t_2\)
❖ Symbols:
  • •
    \(I\) = illuminance
  • •
    \(A\) = area of aperture
  • •
    \(t\) = exposure time
  • •
    \(f\) = focal length of lens
  • •
    \(d\) = diameter of lens
▢ Lamp Above Table:
❖ **table:
    ▢ Illuminance for Different Sources:

    Table 1: Variation of Illuminance with Distance

    Source
    Relation
    Point / spherical source
    \(I\propto\frac{1}{r^2}\)
    Line / cylindrical source
    \(I\propto\frac{1}{r}\)
    Parallel source
    \(I\propto r^0\)
    ▢ Luminance / Brightness:
    ❖ Definition: Luminous flux reflected normally per unit area of surface
    ❖ Formula: Luminance = Illuminance × Reflection coefficient
    ❖ SI Unit: Lambert
    ▢ Eye Sensitivity:

    Table 1: Sensitivity of Human Eye

    Point
    Answer
    Maximum luminous efficiency wavelength
    5550 Å
    Colour
    Yellow-green
    Human eye most sensitive to
    Yellow-green colour
    ▢ Read and Digest:

    Table 1: Important Photometry Points

    Fact
    Answer
    Photometer
    Compares illumination of different sources
    1 phot
    \(1\ lumen/cm^2=10^4\ lux\)
    40 W fluorescent tube vs 40 W bulb
    Fluorescent tube has greater luminous efficiency
    Reason for fluorescent tube efficiency
    For same power, gives more visible light; UV converted into visible light
    Inverse square law valid for
    Point or spherical source
    Condition for inverse square law
    Space free from dust particles
    Search light
    Does not obey inverse square law because beam is parallel
    Sunlight at noon vs morning
    More illuminance at noon because rays fall vertically
    Surface tilted from normal incidence
    Illuminance decreases
    Smoky room
    Illuminance falls faster than inverse square law
    Maximum eye sensitivity
    Yellow-green light, 5550 Å
    Convex lens in film projector
    Makes image brighter
    Phosphorescence
    Re-emission of light after incident light is cut off
    ▢ High-Yield Recall:

    Table 1: Photometry One-Liners

    Fact
    Answer
    Photometry
    Measurement of light energy
    Photometer
    Compares illumination power
    Radiant flux
    Total energy radiated per second
    Radiant flux unit
    Watt
    Luminous flux
    Total visible energy emitted per second
    Luminous flux unit
    Lumen
    1 lumen
    \(\frac{1}{685}\ watt\)
    Luminous flux for sphere
    \(\phi=4\pi L\)
    Luminous efficiency
    \(\eta=\frac{\phi}{R}\)
    Luminous efficiency unit
    Lumen/Watt
    100% luminous efficiency
    685 lumen/watt
    Solid angle
    \(\omega=\frac{Area}{r^2}\)
    Solid angle of sphere
    \(4\pi\)
    Solid angle unit
    Steradian
    Luminous intensity
    \(L=\frac{\phi}{\omega}\)
    Luminous intensity unit
    Candela
    Illuminance
    \(I=\frac{\phi}{A}\)
    Normal illuminance
    \(I=\frac{L}{r^2}\)
    Oblique illuminance
    \(I=\frac{L\cos\theta}{r^2}\)
    Inverse square law
    \(I\propto\frac{1}{r^2}\)
    Lambert's cosine law
    \(I\propto\cos\theta\)
    Illuminance unit
    Lux
    CGS illuminance unit
    Phot
    1 phot
    \(10^4\ lux\)
    Photometry principle
    \(\frac{L_1}{L_2}=\left(\frac{r_1}{r_2}\right)^2\)
    Plane illuminance
    \(I=\frac{Lh}{r^3}=\frac{L\cos^3\theta}{h^2}\)
    Total luminous energy
    \(Q=IAt\)
    Camera exposure time
    \(t\propto\left(\frac{f}{d}\right)^2\)
    Photographic prints
    \(It=constant\)
    Maximum illuminance at table edge
    \(h=\frac{r}{\sqrt2}\)
    Eye most sensitive
    Yellow-green light
    Maximum sensitivity wavelength
    5550 Å
    Search light
    Does not obey inverse square law
    Phosphorescence
    Re-emission after light is cut off
    Q1.
    A bulb is lowered from 4m to 3m above the table. What is change in illuminance?
    📅BP 2014
    Q2.
    The time for photographic print is 10 sec at a distance of 2m from 40 cd lamp. The time required for exposing the same print at a distance of 4m from 20 cd lamp is
    📅BP 2010
    Q3.
    The luminous efficiency of a lamp is 50 lumen/watt and its power is 40 watt. Its luminous flux in lumen is
    📅MOE 2014
    Q4.
    Lumen is an unit representing
    📅MOE 2013
    Q5.
    The illuminance at 10 m directly below a 40 cd lamp is
    📅MOE 2012
    Q6.
    Luminous intensity of light source of illuminance 50 lux at distance of 2m is
    📅MOE 2011
    Q7.
    Two bulbs A and B are placed respectively at 20 cm and 30 cm on opposite sides of an oily paper screen. The two sides of the screen are equally intense. The ratio of power of the bulb A to that of B will be
    📅MOE 2009
    Q8.
    The shutter of camera is opened for 20s at a distance of 2m from the lamp of illuminance of 20 cd. If the distance is made 4m from the lamp of illuminance 40 cd. What is the time of shutter opening?
    📅IOM 2007
    Q9.
    Illuminance at a point 2m from a source of light of luminous intensity 100 candela is
    📅IOM 1997
    Q10.
    The time of exposure of camera is 4 sec. What will be the time of exposure if its aperture is doubled
    📅MOE 2008
    Q11.
    A photographer finds that for a certain aperture of his camera the correct exposure time is 0.25 sec. If the diameter of the aperture is doubled then the exposure time will be
    📅BPKIHS 2007
    Q12.
    The surface area of an electric lamp is 40cm2. If its illuminance at a distance 1m is 2Lm/m2 then the luminous flux from the lamp is
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    Q13.
    The luminous flux from a 100 watt electric lamp is 6850 lumen. The luminous efficiency of the lamp is
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    Q14.
    The luminous efficiency of a lamp is 5 Lumen/Watt. If the luminous intensity is 35Cd, the power of the lamp is
    📅
    Q15.
    What is the ratio of luminous intensity of two sources which produce shadows of equal intensities at distances of 50cm and 100cm from the photometer?
    📅
    Q16.
    The maximum illumination on a screen at a distance of 2 meters from a lamp is 25 lux. The value of total luminous flux emitted by the lamp is
    📅
    Q17.
    The illuminance of a surface 2m away from a point source is 4W/m2. It will be 2W/m2 when the distance of the point from the source is:
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    Q18.
    The Illuminance at a point on a plane surface at a distance of 4m from a bulb is 10-4 lumen/cm2. The line joining the point to the bulb makes an angle of 60° with the normal. The luminous intensity of the bulb is
    📅
    Q19.
    In a cinema hall the distance between the projector and the screen is increased by 2%. If other variables are kept fixed, then the intensity of the illumination on the screen
    📅
    Q20.
    A bulb is situated at a height of 2m above the centre of the table. If the height is decreased by 1m, then percentage change in illumination at the centre of the table will be
    📅
    Q21.
    A 100 watt lamp has luminous intensity 125 candela (isotropic). The luminous flux of the lamp is
    📅
    Q22.
    At what distance 16 candela lamp should be placed from a book so that the illumination received is 1 lumen/m2?
    📅
    Q23.
    Two lamps A and B of 64 and 16 candela respectively are placed 4m apart. At what distance from A should the screen be placed between the lamps so that it is equally illuminated by both the lamps?
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    Q24.
    A 100W lamp is suspended at a height of 5m above the centre of a table. The intensity at the centre of the table in watt/m2 is
    📅
    Q25.
    A small bulb is hanging at a height of 8 feet above the centre of a round table of diameter 16 feet. The ratio of the intensity of illumination at the centre and at points on the circumference of the table will be:
    📅
    Q26.
    The separation between the screen and perfectly reflecting plane mirror is 2r. An isotropic point source of light is placed exactly midway between the mirror and the screen. The ratio of Illuminance on the screen with and without the mirror is:
    📅
    Q27.
    A photographer finds that for a certain aperture of his camera the correct exposure time is 0.25sec. If the diameter of the aperture is doubled, then time of exposure will be
    📅
    Q28.
    The correct exposure time for photographic print is 10sec at a distance of 2m from a 40 C.P. lamp. The time required for exposing the same print at a distance of 4m from 20C.P. lamp is:
    📅
    Q29.
    The exposure time of a camera lens at the f/2.8 setting is 1/200 second. The correct time of exposure at f/5.6 setting is
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