Photometry

1. What are the important concepts of photometry?

Solution:

Photometry is a part of optics that deals with the energy transmitted by light and the visual effects of light.

The most important concepts of photometry are:
a) solid angle
b) luminous flux
c) luminous intensity of a source
d) illumination

Solid angle (Ω) is a cone with its vertex at a point light source, which on a sphere with radius r cuts out an area S.

Ω=Sr2,[Ω]=steradian=sr\Omega = \frac{S}{r^2}, \quad [\Omega] = \text{steradian} = sr

Luminous flux (Φ) is the radiant energy passing through an area S in time t.

Φ=EsS⋅t,[Φ]=W⋅m−2=lumen=lm\Phi = \frac{E_s}{S \cdot t}, \quad [\Phi] = W \cdot m^{-2} = lumen = lm

Luminous intensity (I) is the luminous flux Φ emitted into the solid angle Ω.

I=ΦΩ,[I]=candela=cd,S=4πr2I = \frac{\Phi}{\Omega}, \quad [I] = \text{candela} = cd, \quad S = 4 \pi r^2

Illumination (E) is the luminous flux falling on a unit area.

E=ΦS=lmm2=lux=lxE = \frac{\Phi}{S} = \frac{lm}{m^2} = lux = lx

 E=Ir2cos⁡α,α=0∘⇒E=Ir2E = \frac{I}{r^{2}} \cos \alpha, \qquad \alpha = 0^{\circ} \Rightarrow E = \frac{I}{r^{2}}


where
α\alpha = the angle between the normal of the surface and the direction of light propagation.

 

2.Define:

  • candela
  • lumen
  • lux

Solution:

  • One candela (cd) is 1/600,000 of 1 m2 of the surface of an absolutely black body at the freezing point of platinum (17730C) at normal pressure (101,325 Pa). An absolutely black body is a fictitious body that would absorb all incident radiation.
  • One lumen (lm) is the luminous flux emitted by a point source of luminous intensity one candela into a solid angle of one steradian.
  • A surface has an illuminance of one lux (lx) if a luminous flux of one lumen falls on 1 m2 of that surface.

3. The human eye perceives a light sensation at a minimum retinal illuminance of E=2·10-9 lx. From what maximum distance, under ideal conditions (absolute darkness), can we observe a candle flame with luminous intensity I = 1 cd?

Solution:

Analysis:

physics-photometry-3.gif 

The candle flame can be observed from a maximum distance of 22.4 km.

4.A photometer is illuminated on one side by a light bulb with I1 = 50 cd at a distance r1=0.6 m. On the other side, at a distance r2 = 0.96 m, there is a bulb of unknown luminous intensity (I2 = ?). What is its luminous intensity if the photometer is equally illuminated from both sides?

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5.Above a circular plate with radius r = 0.8 m hangs, at height h1 = 2 m, a light bulb with luminous intensity I = 50 cd. Determine the illuminance

  • a) at the center of the plate
  • b) at the edge of the plate
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6.Two bulbs with luminous intensities I1 = 80 cd and I2 = 200 cd are placed at height h = 2.5 m above a horizontal tabletop. Their mutual distance is d = 3 m. What is the illuminance on the table at the point where the rays from the first bulb strike?

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7. The illuminance of a horizontal surface of the Earth when the Sun’s altitude above the horizon is 450 is E1 = 80,000 lx. Determine the illuminance of the Earth’s surface when the Sun’s altitude is 250.

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8. A wall is illuminated by two identical candles placed right next to each other at a distance of 0.8 m from the wall. By what distance x should one candle be moved closer to the wall if the other goes out (I2 = 0) so that the wall is illuminated the same as before?

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9.A circular area with radius r = 3 m is illuminated by a reflector from a distance h = 60 m. The illuminance of the area is E = 4 lx. Calculate:

  • a) the luminous intensity of the source
  • b) the luminous flux incident on the area
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10. Two light sources with luminous intensities I1 = 25 cd and I2 = 49 cd are placed at a distance d = 1 m. At what point on the line joining them should a screen be placed so that it is equally illuminated by both sources? (I2 is to the left of I1)

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11.Express the units for luminous flux Ф, illuminance E and luminous intensity I using the basic SI units.

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12.Calculate at what distance a lamp with luminous intensity 10 cd has to be placed if an illuminance of 200 lx is required on the worktable and the light falls at an angle of 600.

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13.At a height h = 4 m above the horizontal floor plane there is a point light source with luminous intensity I = 100 cd. Determine the illuminance of the plane at point A, which is at a distance AB = l = 20 m from the foot of the ray that falls from the source perpendicularly onto the plane.

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14.Above a square table with diagonal u = 2.12 m a lamp is hanging at a height h = 1 m. How many times smaller will the illuminance be at the center of the table if we hang this lamp at the same height above one corner of the table?

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15.Which lamp gives greater illuminance? A lamp with luminous intensity 50 cd at a distance of 50 cm, or a lamp with luminous intensity 200 cd at a distance of 200 cm?

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16.At points A and B, which are 165 cm apart, there are point light sources with luminous intensities 36 cd and 25 cd. At which points on the line segment AB is a screen placed perpendicularly to AB illuminated equally by both sources?

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17.A point source has luminous intensity I = 100 cd in all directions. Calculate the total luminous flux and the illuminance of a surface perpendicular to the direction of light and located at a distance of 5 m from the source.

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18.In the center of a hollow sphere there is a point light source. How does the illuminance of the inner surface of the sphere change if the radius of the sphere is doubled?

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19.Calculate what luminous flux falls on an area of 100 cm² from a source of luminous intensity 500 cd, if the area is perpendicular to the rays at a distance of 120 cm from the source.

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20.A school corridor must have illuminance of at least 32 lx at the point directly under the source. The height of the source above the floor is 5 m. How many bulbs with luminous intensity 200 cd must be used?

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