32Photometry

📚
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.
    Choose the wrong statement.
    📅CEE MBBS 2024B
    Q2.
    When distance from a point source is doubled, the illuminance becomes:
    📅CEE MBBS 2023
    Q3.
    Unit of illuminance is:
    📅CEE MBBS 2022
    Q4.
    1 LUX is:
    📅CEE BDS 2021
    Q5.
    A bulb is lowered from a height of \(4 \,\mathrm{m}\) to \(3 \,\mathrm{m}\) vertically above a table. By what percentage does the illuminance at the point directly below it change?
    📅BP 2014
    Q6.
    The time for photographic print is \(10 \,\mathrm{s}\) at a distance of \(2\,\mathrm{m}\) from \(40 \,\mathrm{cd}\) lamp. The time required for exposing the same print at a distance of \(4\,\mathrm{m}\) from \(20 \,\mathrm{cd}\) lamp is
    📅BP 2010
    Q7.
    The luminous efficiency of a lamp is \(50 \,\mathrm{lumen}\)/watt and its power is \(40 \,\mathrm{watt}\). Its luminous flux in lumen is
    📅MOE 2014
    Q8.
    Lumen is an unit representing
    📅MOE 2013
    Q9.
    The illuminance at \(10 \,\mathrm{m}\) directly below a \(40 \,\mathrm{cd}\) lamp is
    📅MOE 2012
    Q10.
    Luminous intensity of light source of illuminance \(50 \,\mathrm{lux}\) at distance of \(2\,\mathrm{m}\) is
    📅MOE 2011
    Q11.
    Two bulbs A and B are placed \(20 \,\mathrm{cm}\) and \(30 \,\mathrm{cm}\) respectively from opposite sides of a photometer screen. Both sides are equally illuminated. Assuming equal luminous efficacy, what is the ratio of their powers?
    📅MOE 2009
    Q12.
    A camera needs \(20 \,\mathrm{s}\) of exposure at \(2 \,\mathrm{m}\) from a \(20 \,\mathrm{cd}\) lamp. What exposure time is needed at \(4 \,\mathrm{m}\) from a \(40 \,\mathrm{cd}\) lamp for the same exposure?
    📅IOM 2007
    Q13.
    Illuminance at a point \(2\,\mathrm{m}\) from a source of light of luminous intensity \(100\) candela is
    📅IOM 1997
    Q14.
    The time of exposure of camera is \(4 \,\mathrm{s}\). What will be the time of exposure if its aperture is doubled
    📅MOE 2008
    Q15.
    A photographer finds that for a certain aperture of his camera the correct exposure time is \(0.25 \,\mathrm{s}\). If the diameter of the aperture is doubled then the exposure time will be
    📅BPKIHS 2007
    Q16.
    An isotropic electric lamp produces an illuminance of \(2 \,\mathrm{lux}\) at a distance of \(1 \,\mathrm{m}\). What is its total luminous flux?
    Q17.
    A \(100\,\mathrm W\) lamp emits \(6850\,\mathrm{lm}\). Assuming maximum luminous efficacy \(683\,\mathrm{lm/W}\), find its luminous efficiency.
    Q18.
    An isotropic lamp has a luminous efficacy of \(5 \,\mathrm{lm}/\,\mathrm{W}\) and luminous intensity of \(35 \,\mathrm{cd}\). What is its electrical power?
    Q19.
    What is the ratio of luminous intensity of two sources which produce shadows of equal intensities at distances of \(50\,\mathrm{cm}\) and \(100\,\mathrm{cm}\) from the photometer?
    Q20.
    The maximum illumination on a screen at a distance of \(2 \,\mathrm{m}\) from a lamp is \(25 \,\mathrm{lux}\). The value of total luminous flux emitted by the lamp is
    Q21.
    The irradiance from a point source is \(4 \,\mathrm{W}/\,\mathrm{m}^2\) at \(2 \,\mathrm{m}\). At what distance is it \(2 \,\mathrm{W}/\,\mathrm{m}^2\)?
    Q22.
    At a point on a plane surface \(4\,\mathrm{m}\) from a bulb, the illuminance is \(10^{-4}\,\mathrm{lumen/cm^2}\). The ray makes an angle of \(60^\circ\) with the surface normal. Find the luminous intensity of the bulb.
    Q23.
    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
    Q24.
    A bulb is situated at a height of \(2\,\mathrm{m}\) above the centre of the table. If the height is decreased by \(1\,\mathrm{m}\), then percentage change in illumination at the centre of the table will be
    Q25.
    A \(100 \,\mathrm{watt}\) lamp has luminous intensity \(125\) candela (isotropic). The luminous flux of the lamp is
    Q26.
    At what distance \(16\) candela lamp should be placed from a book so that the illumination received is \(1 \,\mathrm{lumen}/\,\mathrm{m}^2\)?
    Q27.
    Two lamps A and B of \(64\) and \(16\) candela respectively are placed \(4\,\mathrm{m}\) apart. At what distance from A should the screen be placed between the lamps so that it is equally illuminated by both the lamps?
    Q28.
    A \(100 \,\mathrm{W}\) isotropic point source emits all its power as radiation. It is \(5 \,\mathrm{m}\) above a table. What is the irradiance directly below it?
    Q29.
    A small bulb is hanging at a height of \(8 \,\mathrm{feet}\) above the centre of a round table of diameter \(16 \,\mathrm{feet}\). The ratio of the intensity of illumination at the centre and at points on the circumference of the table will be:
    Q30.
    A perfectly reflecting plane mirror and a screen are separated by \(2r\). An isotropic point source is placed midway. What is the ratio of illuminance on the screen with and without the mirror?
    Q31.
    A photographer finds that for a certain aperture of his camera the correct exposure time is \(0.25\,\mathrm{s}\). If the diameter of the aperture is doubled, then time of exposure will be
    Q32.
    The correct exposure time for photographic print is \(10\,\mathrm{s}\) at a distance of \(2\,\mathrm{m}\) from a \(40 C.P.\) lamp. The time required for exposing the same print at a distance of \(4\,\mathrm{m}\) from \(20C.P.\) lamp is:
    Q33.
    The camera exposure time at \(f/2.8\) is \(\frac{1}{200}\,\mathrm{s}\). What is the exposure time at \(f/5.6\)?