## Abstract

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Full Article | PDF Article**Journal of the Optical Society of America**- Vol. 30,
- Issue 3,
- pp. 133-135
- (1940)
- •doi: 10.1364/JOSA.30.000133

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The quartz mercury arc lamp used in these experiments is enclosed in a heavy water-tight casing made strong enough to withstand immersion of 10 meters or more in sea water.

The arc stream, here shown in exaggerated proportions, is considered to be a square-ended cylinder, but the indicated angles are measured not from the edge but from the axis of the cylinder. The water here acts as a positive lens, increasing the apparent size of the arc.

The water between the cell and the lamp casing forms a plano-concave lens, and the apparent diameter of the arc stream is decreased.

The upper curve is a trial plot of the transmission factors, and the extrapolation to zero length of path through water leads to a pseudo transmission of 1.16. When this point is brought down to 1.00 the final transmissions are as shown by the lower curve. The increasing transmission per unit length as the total path length increases is a clear indication of the nonhomogeneous nature of the arc radiation.

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$${A}_{0}=KB{\omega}_{0},$$

$${A}_{1}=KB{\omega}_{1}t,$$

$$t=\frac{{A}_{1}{\omega}_{0}}{{A}_{0}{\omega}_{1}}.$$

$$i=nr,$$

$$za+\frac{zw}{n}+zb=S,$$

$$z=S/\left(a+\frac{w}{n}+b\right).$$

$$(x-ny)a+\left(\frac{x}{n}-y\right)w=yb.$$

$$\begin{array}{l}(x-ny)a+(x-ny)\frac{w}{n}+\frac{xb}{n}=yb+\frac{xb}{n},\\ (x-ny)a+(x-ny)\frac{w}{n}+(x-ny)\frac{b}{n}=\frac{xb}{n},\\ (x-ny)=xb/(an+w+b).\end{array}$$

$$\begin{array}{l}\omega =4z(x-ny)\\ =4Sbx/(an+w+b)\left(a+\frac{w}{n}+b\right).\end{array}$$

$$x=R/b,$$

$$\omega =4SR/(an+w+b)\left(a+\frac{w}{n}+b\right).$$

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