PROBLEMS 357 



dptr. The distance of the anterior principal point of the eye from the second princi- 

 pal point of the spectacle lens is 12 mm. What is the refraction of the eye? 



Ans. +11.4 dptr. 



Ill— 7. In Gullstrand's schematic eye, with accommodation relaxed, the distance 

 from the image on the retina to the apex of the cornea is 24 mm. A correcting 

 spectacle lens of 5.+dptr refracting power is used with its second principal point 

 14 mm from the anterior principal point of the eye. What is the length of the eye- 

 ball? What is the static refraction? 



Ans. 26.5 mm; +1.01 dptr. 



Ill— 8. A common form of " magnifying lens " consists of a +12.0-dptr lens. 

 What is its magnifying power? 



Ans. 5. 



III-9. A myoptic eye of 10 dptr uses a reading glass of 5-cm focal length. Neg- 

 lecting the distance from eye to glass, what is its magnifying power? 



Ans. 7.5 X. 



Ill— 10. The refracting power of an eye is 58 dptr. What is the size of the retinal 

 image of an object 200 cm high at a distance of 12 meters? 



IV- 1. The intensity / of a beam of radiant energy in passing through an absorb- 

 ing liquid decreases according to the empirical relation / = 20e~ 100d , where d is the 

 depth in centimeters. Draw the semilogarithmic graph of / as a function of d. 

 From this graph interpolate the intensity and its rate of change when the intensity 

 has fallen to 0.1 of its incident value. 



Ans. 0.001, -0.1. 



IV-2. A given solution of copper chloride, 1.006 cm thick, absorbs 18.1 per cent 

 of the light (5510 to 5540 A) incident upon it. What percentage will be absorbed 

 by a layer of this solution 7.64 cm thick? 



Ans. 78.1 per cent. 



IV-3. A population of a colony of bacteria is observed to increase at a rate of 

 5 per cent per day of the number then living. If the population is initially 100,000 

 what is the population after 10 days? 



Ans. 164,870. 



IV-4. It was found that the percentage of the survivors of a radiated colony of 

 organisms was constant during an experiment regardless of the number of cells 

 present. The experiment showed that at time 0, 1, 2, 3, 4, 5, and 6 the survivors 

 numbered 10 6 , 10 5 , 10 4 , 10 3 , 10 2 , 10, and 1. How many died per day? What 

 percentage died per day? Compute the death rate K where 



where a is the initial number and b the number after time t. 



IV-5. The growth of Bacterium coli on broth was observed to be 19,000 at 

 10 a.m., 35,900 at 10:30, 88,000 at 11:00; subsequent data taken at hourly intervals 

 gave 482 X 10 3 ; 3.40 X 10 6 ; 26.3 X 10 6 ; 71.6 X 10 6 ; and 118 X 10 6 counts. 

 What is the form of the growth curve? Which portion of the curve indicates that the 

 nutrients available for growth decreased as the number of organisms increased? 



V-l. If the surface energy of water at 0° C is 75.796 ergs/cm 2 , what is it at 20° C? 



V-2. What is the total potential surface energy of each of three drops of water 

 whose diameters are 0.2, 0.4, and 0.6 mm? If they are brought in contact to make a 

 single drop, what is the surface energy? How do you account for the difference? 



