Jin Wu 
in the longitudinal direction is about 1°; see figure 2, 
The focal spot of the telescope on the water surface is circu- 
lar, with 0.7-mm diameter. This spot is completely bright when the 
water surface is relatively flat and is partially bright when the curved 
water surface reflects part of the impinging light away from the teles- 
cope. Simple calculations have been made along with a calibration 
test consisting of passing cylinders, with the same kind of reflecting 
surface but with various radii, under the instrument. The longitudi- 
nal axis of the cylinder is always parallel with the same axis of the 
lamp. From the geometry in figure 3a, the following relationships 
can be obtained for a curved surface with radius of curvature R: 
a Tog = HK Ccos. a li, - R cos, & 
2a = cot a aaa COL SSeS aL ee (1) 
w/2+R sin a d/2+ Rsin a 
for a convex surface, and 
Lp + Rcosa 1 ei COSme 
=f = t 
Zo = Ceot + cot 7 (2) 
w/2+R sina d/2 +Rsin a 
for a concave surface, where d is the diameter of the pinhole located 
in front of the photomultiplier, wis the effective width of the plano- 
convex cylindrical lens for focusing the light, and L,and Ly are the 
distances from the telescope and the light box lens to the mean water 
surface, respectively. Only single reflections are considered. 
By choosing the size of the pinhole to be much smaller than 
the beamwidth of the light and by putting the instrument away from 
the surface (for the present setup, w/d = 400 and L/w = L,/w = SO). 
we can show that the second term on the right of (1) and (2) is much 
smaller than the first term in each respective equation. In other 
words, by the proper setting of the distance between the instrument 
and the water surface ( Lp >> R), both (1) and (2) can be approxima- 
ted by 
a = 
leenwis a 
2 t [Le / ( /2)] (3) 
Hence, the response of the instrument to surface curvature is essen- 
tially the same for both concave and convex surfaces. 
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