V. Voss. The ratio of the intensities of the D lines of sodium.

V. Voss. The ratio of the intensities of the D lines of Sodium.

(The Physical Review, Vol. XI, January 1918, p. 21).

It is known that the ratio of the intensities of the \(D\) lines depends on the change in the intensity of the sodium flame. The first indications of this kind are found in Gouy, who showed that \(\dfrac{D_2}{D_1}\) changes from 1.3 for a bright flame to 2 for a weak flame.

Wood’s observations showed that for an extremely weak flame this ratio reaches the value 3 or even 3.5. This ratio was obtained by comparing photographs at different exposure times, on the assumption that the blackening of the photographic plate is directly proportional to the exposure time.

This discrepancy in the values led the author to measure the ratio $\dfrac{D_2}{D_1}$ more carefully. For this purpose he used three methods.

1) A photographic method, using a special sector disk which made it possible to divide the field of view into 7 transverse strips.

2) A visual method, in which the intensities were compared by means of the polarization method.

3) A visual method, in which screens having a definite coefficient of absorption were used.

I. The sector disk was arranged in such a way that the exposure times for successive strips were in the ratio $5:4$. The slit of the spectrograph was shifted so that both lines $D_2$ and $D_1$ touched, and the image on the photographic plate was obtained in the form of a rectangle. The plate was then cut across, and the two halves were compared for blackening. In this way it was found that $\dfrac{D_2}{D_1}=1.25$ for a bright flame and $\dfrac{D_2}{D_1}=3$ for a weak flame.

The decrease of the ratio $\dfrac{D_2}{D_1}$ with increasing flame intensity can be explained by the greater absorption of the light corresponding to the line $D_2$. The slit of the spectroscope was illuminated by a weak sodium flame and was opened until the lines $D_2$ and $D_1$ were no longer touching. A glass sphere, annealed and containing a small quantity of sodium, was placed between the flame and the slit. The sphere was heated, the sodium evaporated. The value of the ratio for the weak flame immediately fell to the value found for the intense flame.

II. In the polarization method he used Wood’s method1 for separating the lines $D_2$ and $D_1$, without reducing their intensities, by means of a quartz plate 32 mm thick. Comparison of the intensities in this case is rather difficult, but nevertheless it may be asserted that here too the most accurate value for the ratio $\dfrac{D_2}{D_1}$ is 2.

III. In the third method Voss used screens, one of which transmitted $33\frac{1}{3}\%$, another $40\%$, and the third $50\%$ of the incident light. Three narrow strips of these screens were placed in the cassette of the spectrograph, whose slit was illuminated by a sodium flame. One half of the image in the form of a rectangle, obtained from the contact of the lines $D_2$ and $D_1$, could be covered by moving the cassette with one or another screen. In this way it was easy to detect the difference in the ratio when $D_2$ was covered by the 40% screen, as compared with when it was covered by the 50% screen. Thus, it may be considered that the ratio $\dfrac{D_2}{D_1}=2$ with an accuracy up to 10%. The author notes that this method is the most deserving—

degree of confidence in all three. Here a discrepancy is obtained between methods I and II. In the first, for a weak flame we have a ratio \(=3\), while in the second \(=2\).

In order to clarify this discrepancy, Voss constructed an “artificial slit,” namely, he cut a rectangular opening in cardboard, covered it with a screen transmitting yellow light corresponding to the line \(D\). Half of the “slit” was covered with a screen absorbing 50% of the incident light (as in the third method). The slit was placed between a sodium flame and a photographic camera. After a series of exposures an extremely curious result was obtained: the ratio of the exposure times for the two halves was found to be \(3:1\), i.e. exactly the same as was obtained with a weak flame for the lines \(D_2\) and \(D_1\).

But if the “slit” is illuminated with a tungsten lamp, the ratio obtained is \(2:1\).

It is clear that such a difference cannot be explained by a change of \(K\) in Schwarzschild’s law (\(S=Jt^k\), where \(S\) is the density of the image, \(J\) the intensity of light, \(t\) the exposure time, and \(K\) a quantity depending on the kind of plate and on the wavelength of the light), since the range of change of the wavelength in the given case is very small.

Thus, here we are apparently dealing with the very curious behavior of the photographic plate with respect to white and monochromatic light.

Of all three methods, taking this last circumstance into account for the first, it may be asserted that the maximum value of the ratio of the intensities of the sodium \(D\) lines is

\[ \frac{D_2}{D_1}=2 \]

with an accuracy of up to 10%.

T. Molodoi.

1. Wood. ↩