958 
(e) 
It is felt that this deviation from Snell's Law is not important for the case 
of non-polarized light in water. However, in order to make a quantitative statement 
as to the amount of possible error, a further analysis would have to be made. 
An experimental argument for the assumption that this deviation from Snell's 
Law is not important for the case of the shock-wave study in water is that, in 
several calculations of the time constant based on rays of light which are observed 
to strike the lucite grid at varying distances from the point of total reflection, 
no systematic trend can be detected with the distance of the point of observation 
from the point of total reflection. 
Sample calculation of time-constant, -- As an example of the time-constant 
calculation, the data for Point 22, Film 536 (Fig. 111) will be developed. 
The first step is to obtain nas a function of r for a given film. The data 
necessary for this are given in Table VIII which shows data from film No.'s 536 
and 537 for comparison. 
Table VIII Constants Necessary for Ea, (II-15) 
Film 536 Film 337 
Kind of Film Contrast Process Ortho Contrast Process Ortho 
Temperature 21.3° C. 17.1° C. 
a 14.94 x 10-6 per atmos- 15.18 x 10-6 per atmos- 
phere phere 
b 001578 x 10-6 per atm.2 001578 x 1076 per atm.2 
Do 153435 1.3444 
{RI 15.97 in. 15.99 in. 
17,050 1b/in® = 1,160 atm. 17,050 lb/in® = 1,160 atm 
When the proper values of n,, a, b, and Pnax from Table VIII for Film 536 are 
substituted in Eq. (II-15) it becomes 
n= 1.3435 + .017328% (17x) - .002122866 ~ (=x) (11-32) 
where 
x= am = = 
(Ri RI 
since throughout all calculations, measurements in units of [R{ were used. 
Then, since for any pair of intersections, 
sin i, Qo 
sin @ DR 
from Eq. (II-16) 7 sin ig = ny sin @, The value of n, is known for a given film 
(Table VIII) and sin @ was found for each point in tho calculation for Pays Thus, 
for Film 536, Pt. 22, np sin ig = ny sin @ = (1.3435) (.93154) = 1.25152. 
Substituting for n and for np sin ig the values obtained in the preceding 
paragraphs, one obtains the differential equation of the path of the ray of light 
considered at point 22, 
wd 15518 
