2 ELEMENTARY PRINCIPLES OF MICROSCOPICAL OPTICS 



found by published tables. A table to quarter degrees is given in 

 Appendix A of this book, which will, in the majority of cases. 

 suffice ; it is not difficult to find such tables as may be required. 1 



Of course it is more than desirable that the microscopist should 

 have good mathematical knowledge ; but there are many men who 

 desire to obtain a useful knowledge of the principles of elementary 

 optics who are without time or inclination, or both, to obtain the 

 large mathematical knowledge required. 



Now, just as a man who is without any accurate knowledge of 

 astronomy or mathematics may find time from a sun-dial by applying 

 the equation of time taken from a table in an almanac, so by' the 

 use of a table of sines the microscopist may reach useful and reliable 

 results, although he may have no clear knowledge of trigonometry, 

 physical optics, nor the mathematical proof of formula?. 



All microscopes, whether simple or compound, in ordinary use 

 depend for their magnifying power upon the ability possessed by 

 lenses to refract or bend the light which passes through them. Re- 

 fraction acts in accordance with the two following laws, viz. : 



1. A ray which in passing from a rare medium into a denser 

 medium makes a certain angle with the normal, i.e. the perpendicu- 

 lar to the surface or plane at which the two media join, will, on 

 entering the denser medium, make a smaller amjl' /<///, //,,; normal. 

 Conversely, a ray passing out from a, dense medium into a rarer one, 

 making a certain angle with the normal, will, on emergence from 

 the dense medium, make a greater angle with the normal. 



The ray in one medium is called the incident ray, and in the 

 other medium the refracted ray. 



The incident and refracted rays are always in the same plane. 



2. The sine of the angle of incidence divided by the sine of the 

 angle of refraction is a constant quantity for any two particular 

 media. 



When one of the media is air (accurately a vacuum) the ratio of 

 these sines is called the absolute refractive index of the medium. 

 As every known medium is denser than a vacuum, it follows that 

 the angle of the refracted ray in that medium will be less than the 

 angle of the incident ray in a vacuum ; consequently, the absolute 

 refractive index of any medium is greater than unity I 



Further, the absolute refractive index for any particular suit- 

 stance will differ according to the colour of the ray of light employed. 

 The refraction is least for the red. and greatest tin- the violet. The 

 difference between these refractive values determines what is called 

 the <//.s-/wr.s'/Yr jxm-i'i- of 1 lie substance. 



This will be understood by fig. I. Let 1 ('. a ray of lijrht travel- 

 ling in ;iir. m. 'ei the "surface A B of water ai the point C. Through 

 ' dra\\ X' .-it right angles to the surface of the water A Ix The 

 lino X : ' is culled the ,,<>r;i<ii! to the surface A B. The ray I C' \\ill 

 not continue its p.-ith through the \\ater in a straight line to Q ; but. 

 because water i> denser than air, it will be bent to R. that is 

 towards N'. The whole course of the ray will be I C R, of which 

 the part I C is called the incident r</?/. and C R the refracted ray. 

 1 I ' bambi i Mathematical Tab/< ;. 



