MAY, 1936

Photographic Penetration of HazeNORA M. MOHLER, Smith College

(Received February 7, 1936)

Photographs taken with panchromatic and with infrared plates yield visibility ratios whichrange from 1.1 for days with thick haze or light rain, to 1.7 for clear days (visibility 20 miles).These values indicate an upper limit of 0.3ku for the radius of drops in the thin haze.

THE penetrating power of infrared plates incomparison with panchromatic plates was

used by E. 0. Hulburt in a study of the attenua-tion of light in clear and foggy atmospheres.'His results are given for visibilities up to eightmiles. This report extends the results to an eyevisibility of about twenty miles.

The photographs were taken in the Con-necticut valley, from the Mt. Tom range, lookingnorth in most cases. Estimates of visibility weremade visually and from the plates by noting themost distant distinguishable object, and checkingthe distance on a topographic map. Curves inthe Connecticut River are the features noted ondays of low visibility; the rather abrupt hillswhich occur in the Northampton to Greenfieldsection of the valley offer a number of easilyidentified points for distances up to fifteen miles;the range of hills beyond Greenfield yield possiblebut less surely identifiable points to over thirtymiles. The valley has little manufacturing and nodust or smoke haze is noticeable over the towns.

Photographs were taken on Wratten andWainwright panchromatic plates and on TypeIR infrared plates, each with an A filter, No. 25,red. Visibility with the former is practicallyidentical with that of the eye.

The results are given graphically. The slopeof the curve changes steadily from 1.1 for daysof low visibility to 1.7 for the clearest days.The agreement between points for hazy days andfor days of continuous or intermittent rain, isstriking.

From two of the formulas and Fig. 1 of thearticle referred to, rather interesting conclusionsmay be drawn, in connection with the value ofthe slope. The intensity of light of a certainwave-length is given by the formula

I E. 0. Hulburt, "Attenuation of Light in the LowerAtmosphere," J. 0. S. A. 25, 125 (1935).

i = ioe-(a+#+z)x (1)

in which io is the original intensity of the light,and i its intensity after passing through thedistance x, and i3 are scattering and absorptioncoefficients due to air molecules, and y theattenuation due to foreign particles, chieflywater drops and dust. It has been shown thatfor particles of index of refraction 1.33,

y = 7rr'nk, (2)

in which r is the radius of the particles, n theirnumber per cc, and k a function of X/r. This

3or

2

20

15

1 0

5

((1

,-JI-

- Im

-Lia:_U

cr_ 0LL

z /

+/

E YE

5

0

0 HAZE+ SHOWERS

+

+

VISIBILITY10

FIG.

(M LES)

15 20

219

J. O . S. A. V OL UM E 2 6

220 NORA M.

function is given graphically in the figure re-ferred to.

It follows from Eqs. (1) and (2), that if a and3 are small with respect to y, which is true for

wave-lengths longer than 300 mz, two photo-graphs taken under the same conditions exceptfor the effective wave-lengths, will show visi-bilities inversely proportional to B-y; if one sizeof drop is chiefly responsible for the effect theranges will be inversely proportional to thek's also.

The ratio of visibilities runs from 1.7 for cleardays, through 1.4 for hazy days, to 1.1. The ratioof wave-lengths for the two plates is about 6 to 8,as the filter cuts at 580 m and the panchromaticplate is quite insensitive beyond 650 mju, andthe R sensitivity is chiefly from 740 to 840 mu.Two parts of the k curve show decreasing k with

MOHLER

increasing X/r. For X/r < 1 the slope yields a valuefor ki/k 2 of about 1.5 for a wave-length shift inthe ratio of 1 to 1.3 (r assumed constant). A shiftto somewhat greater or smaller values of X/r de-creases the ratio. For values greater than 1, theratios of k increase from 1.1 for X/r about 1 to1.7 for 2< X/r<5, for the same change in wave-length. These correspond to values of r from 0.1to 0.3y for thin haze, to 0.6it for thick haze, withphotographic conditions duplicated in the middlerange for particles of 3M radius. The presence oflarger particles with the smaller changes the 2eyvalues and may degrade the slope, but the upperlimit of 0.3,4 for the particles in thin haze seemsdefinite. Hence thickening haze means a changein r as well as in n, with a slight change in sizefor most of the drops, or with an addition ofcomparatively few much larger drops.