64 LIGHTING AND FOCUSING [ CH. II 



? in. Critical Angle and Total Reflection. In order to understand the 

 Wollaston camera lucida (Ch. IV) and other totally reflecting apparatus, it is 

 necessary briefly to consider the critical angle. 



The critical angle is the greatest angle that a ray of light in the denser of 

 two contiguous media can make with the normal and still emerge into the 

 less refractive medium. On emerging it will form an angle of 90 with the 

 normal, and if the substances are liquids, the refracted ray will be parallel 

 with the surface of the denser medium. 



Total Reflection. In case the incident ray in the denser medium is at an 

 angle with the normal greater than the critical angle, it will be totally reflected 

 at the surface of the denser medium, that surface acting as a perfect mirror. 

 By consulting the figures it will be seen that there is no such thing as a 

 critical angle and total reflection in the rarer of two contiguous media. 



To find the critical angle in the denser of two contiguous media : 



Make the angle of refraction (i. e., the angle in the rarer of the two 



/sin i\ / index r \ 



media) 90 and solve the general equation :( -) = (-; r ). I v et the 



\sm r/ \ index i / 



two substances be water and air, then the sine of r( 90) is i, and the index of air 

 is i, that of water 1.33, whence/ - j=f - - j or sin z 751 + . This is 



the sine of 48+, and whenever the ray in the water is at an angle of more 



than 48 it will not emerge into the air, but be totally reflected back into 



the water. 



The case of a ray passing from crown glass into the water : 

 / sin i X^/ index water (1.33) \ Qr /sin_'\ _/_i.33\ 



\ sin r (sin 90 -i)/ ~~\ index glass (1.52)7 \ i / ' \ 1.52 /' 



whence sin i .875 sine of critical angle in glass covered with water. The 



corresponding angle is approximately 61. 



\ 112. Color Images. These are images of objects which are strongly 

 colored and lighted with so wide an aperture that the refraction images are 

 drowned in the light. Such images are obtained by removing the diaphragm 

 or by using a larger opening. This method of illumination is especially 

 applicable to the study of deeply stained bacteria. (See below 119.) 



ADJUSTABLE, WATER AND HOMOGENEOUS OBJECTIVES : 

 EXPERIMENTS 



. \ 113. Adjustment for Objectives. As stated above (% 27), the aberration 

 produced by the cover-glass (Fig. 64), is compensated for by giving the com- 

 binations in the objective a different relative position than they would have if 

 the objective were to be used on uncovered objects. Although this relative 

 position cannot be changed in unadjustable objectives, one can secure the 

 best results of which the objective is capable by selecting covers of the thick- 

 ness for which the objective was corrected. (See table 33.) Adjustment 

 may be made also by increasing the tube-length for covers thinner than the 



