54 LIGHTING AND FOCUSING [CH. II 



water and glass, the incident light being in water the formula would be : 



( ) = ( — : — I • If the incident ray were in glass and the refracted ray in 



\sin rj V i-33 / 



water : ( — ) =• ( ) • And similarly for any two media ; and as stated 



\sin rj \ 1.52 / 



above if any tbree of the factors are given the fourth may be readily found. 



\ 100. Critical Angle and Total Reflection. — In order to understand the Wol- 

 laston 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 refrac- 

 tive 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 consult- 

 ing 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 (z. e. , the angle in the rarer of the two media) 



• / sin 1 \ / index r \ 



qo° and solve the general equation : ( — I = I -■ — ; r ) . Let the two sub- 



\sin r J \ index 1 / 



stances be water and air, then the sine of r (90 ) is 1, the index of air is 1, that of 

 water 1.33, whence ( ) = ( ) or S1 V z = 75 I_ K This is the sine of 



48° + , and whenever the ray in the water is at an angle of more than 4S 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 \ /index water ( 1.33) \ / sin i \ / 1.33 \ 



\sin r (sin 90°= 1) / ~~ \ index glass (1.52) / \ 1 / V1.52/ 

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

 corresponding angle is approximately 6i°. 



\ 101. Color Images. — These are images of objects which are strongly col- 

 ored 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. § 108). 



ADJUSTABLE WATER AND HOMOGENEOUS OBJECTIVES 

 EXPERIMENTS 



I 102. Adjustment for Objectives. — As stated above (§ 24), the aberration 

 produced by the cover-glass (Fig. 57), is compensated for by giving the combina- 

 tions 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 



