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Visual Perception and Photometry

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The eye, like our other sensory organs, has been the object of much physiological and psychological research. Nevertheless, physicists must also be aware of the more important properties of their sense of visual perception.

In physics, we classify radiation according to its radiant power \(\dot{W}\). (We also call this quantity the radiant flux to emphasize the “flow” of energy carried by a beam of radiation, e.g. towards a receiver; see Chap. 19). Figure 15.4 showed the measurement of radiant power in one of the usual units, e.g. in watt. The radiant power \(\mathrm{d}\dot{W}\) as defined there is contained within a solid angle \(\mathrm{d}\Omega\). Then we define the

$$\displaystyle\text{Radiant intensity\ }I_{\vartheta}=\frac{\text{Radiant power\ }\mathrm{d}\dot{W}_{\vartheta}}{\text{Solid angle\ }\mathrm{d}\Omega}\,. $$

The radiant intensity (or simply intensity) is thus measured in physics as a derived quantity with the unit 1 W/sr.

For the sense of visual perception, the physical radiant power and the quantities derived from it (Chap. 19) are not relevant. Our visual sense responds to radiant power only very selectively in a small region of the electromagnetic spectrum. Therefore, a method of measuring the radiation had to be found in which the radiant power is evaluated only in terms of its effect on the human eye, i.e. on our visual perceptions (photometry). The fundamentals of photometry will be treated in Sects. 29.2 through 29.7.

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  1. 1.

    Candela (the second syllable is stressed) is the Latin word for candle. The luminous intensity is thus denoted by the same word that refers to a commercially-available object, for example a light from burning wax.

  2. 2.

    Of course, one could introduce other physical quantities which can be related to our visual perception sense as base quantities, for example the luminous density or photometric brightness (now called the “luminance”), i.e. the radiance as perceived by the eye. Then the luminous intensity would become the derived quantity luminance ⋅ source area, etc. The use of the luminous intensity as base quantity makes it experimentally simpler to develop the photometric measurement procedures.

  3. 3.

    The limiting frequency is, from experience, smallest when the durations of the dark and light intervals are equal. (In motion-picture films, about 0.01 s. Every image is projected twice and only every second dark interval is used to change to the next image ; the image frequency is thus 25 Hz.)

  4. 4.

    One would have to give preference to the definition whose results best obey an additivity rule. Illuminances are additive; for example, following one of the methods described, we determine two illuminances A and B. When added, they yield the illuminance C = A + B. When a direct measurement by the same method also gives the value C, we can say that the method obeys the additivity rule. In this sense, definition no. 4 appears to be the best.

  5. 5.

    Corresponding to roughly 100 light quanta/second.

  6. 6.

    In astronomy, the distance unit ‘parsec’ is equal to that distance R 0 from which the radius of the earth’s orbit r would be seen to subtend an angle of \(1^{\prime\prime}\), that is

    $$\displaystyle R_{0}=r/1^{\prime\prime}=1\,\text{parsec}=3.08\cdot 10^{16}\,\text{meter}$$
    $$\displaystyle(1^{\prime\prime}=(1/3600)^{\circ}=4.85\cdot 10^{-6}\,\text{rad},r=1.49\cdot 10^{11}\,\text{m}).$$
  7. 7.

    The parallax α of a fixed star is defined as the angle

    $$\displaystyle\alpha=\frac{\text{Radius of earth's orbit}\,r}{\text{Distance to the fixed star}\,R}\,.$$

    From Eqns. (29.6) and (29.8), we find that a fixed star with a parallax α is at a distance

    $$\displaystyle R=\frac{1^{\prime\prime}}{\alpha}\cdot R_{0}=\frac{1^{\prime\prime}}{\alpha}\,\text{parsec}$$
  8. 8.

    The formation of brown shades can be demonstrated by quite simple means. A circular disk has three glued-on sectors of colored paper, around 210\({}^{\circ}\) of black, 90\({}^{\circ}\) of red, and 60 ° of yellow. It is rotated rapidly. The motion causes the three individual colors to vanish and ‘merge’ together into a unified brown.C29.4

  9. 9.

    For the purple hue, we need two narrow slits, one in the blue or in the violet region, and the other one in the red.

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Correspondence to Klaus Lüders .

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Lüders, K., Pohl, R.O. (2018). Visual Perception and Photometry. In: Lüders, K., Pohl, R. (eds) Pohl's Introduction to Physics. Springer, Cham.

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