COLOURS OF THIN PLATES.] 



UNDULATORY FORCES. LIGHT. 



51 



Experiment 1. Place a glass lens, of a focal length ol 

 ten or twelve feet, on a flat plate of glass, and press the 

 two surfaces together. It will be observed, that if great 

 pressure be employed, a small dark spot will be produced 

 at the point where the two surfaces are nearest each 

 other ; and round tlus point a series of concentric circles 

 will be formed, each being of a definite colour, and varying 

 from violet to red. 



Experiment 2. Boil some water in a Florence flask, 

 or other glass vessel, and throw into it a pea of Castille 

 soap. When steam issues from the neck of the vessel, 

 and all the air has been expelled, cork the flask so that 

 it sliall be air-tight. On shaking up its contents, thin 

 films will be formed, presenting a similar set of appear- 

 ances to those named in the last experiment. 



Now, the production of these colours is due to the fact, 

 that the plate of air or film of the soap-bubble is of 

 exactly the thickness required to produce the colours 

 observed. If the plate be exceedingly thin, then no light 

 will be reflected, and the spot will be black. If somewhat 

 thicker, then violet light will be perceived; and so on 

 until the plate becomes of greater substance, when red 

 light will be reflected from the surface, and so reach 

 the eye. 



If, however, the observer look throuyh, instead of at, 

 the plate of glass, he will see what are called the comple- 

 mentary colour*, which, combined with the colour observed, 

 would produce white light. These experiments enable 

 > tell the thickness of a plate of air ; and, therefore, 

 the length of an undulation of light of any colour ; for 

 we have only to learn the distance between the lens and 

 the flat glass at any point where we notice a colour 

 whose undulation we wish to study, when the length of 

 the undulation is of course obtained. This is easily done ; 

 for, knowing the size of the circle of which the lens forms 

 part, we can at once learn the length of any arc of that 

 circle, and, taking the length of the tangent of that arc 

 in which we observe the undulation existing, we can 

 obtain the thickness of air between the tangent and the 

 curve of the circle. 



This will be easily understood by referring to Fig. 26, 



in which a 6 represents a 

 flat glass plate, resting 

 gainst a lens d d, which 

 forms part of a sphere 

 whose centre is e. Let 

 / / be the extremities of 

 a ring of coloured light 

 distant from e, which is a 

 point where we will sup- 

 pose a black spot, or place 

 where no light is reflect- 

 ed T / is, of course, the 

 tangent of the angle fee. 

 Now / g, the thick- 

 ness of the plate of air, 

 will evidently depend on the angle wliich / forms with 

 the radius of the circle c e. The length of c e, e g, being 

 lily obtained by ordinary measurement, / g is, of 

 course, as easily found. It follows, that the smaller 

 the angle existing with respect to the centre of the 

 circle c, the thinner will be the plate of air between 

 the lens and the glass plate o 6. As the measurement 

 of all intermediate distances involves only the ordinary 

 rules of mathematics, the student will at once perceive 

 that we can thus calculate the thickness of any coloured 

 plate, and, therefore, infer the length of an undulation 

 of any ray of light under examination. 



We have thus endeavoured to explain how we are 

 enabled to measure the thickness and length of these 

 plates of air ; and having once ascertained the facts of 

 the case, their general application is easily arrived at. 

 Thus, if we observe that a soap or oil film presents the 

 same colour as that which we find at any part between 

 the lens and the glass plate, we at once infer that the 

 thickness of each is equal. There is, however, a limi- 

 i of the law, which we must carefully bear in mind. 

 It U, that the thickness of plates of different materials 

 reflecting the same coloured light, is inversely as the 



ratio of their index of refraction. Hence plates of vari- 

 ous transparent media, such as air, water, glass, oil of 

 cassia, <tc., are of different thicknesses when producing 

 similar optical coloured effects. 



We append a rough illustration of the position of the 

 colours as observed between the lens and the plate, and 

 a table of the thickness of the coloured plates ; but must 

 here state, that for the sake of simplicity, we have con- 

 fined the attention of the reader to the production of 

 only one order of rings. There are, however, several of 

 these produced. The relative thicknesses and positions 

 of the first order are y . 2 , 



pointed out below, 

 and represented in 

 the annexed engrav- 

 ing. In Fig. 27, o 

 represents the lens 

 placed on the glass 

 plate 6, and c is the 



interval existing be- 543212S44 



tween the two. In the annexed table, the numbers in 

 the figure above indicate the position of the reflected 

 colours placed before them ; and the thicknesses of these 

 are also given for the series of rings, commencing from 

 the nearest or central point of contact. 



Colour. Thickness in parts of an inch. 



No. 1 ... Black 000005 



2 . . . Blue 000024 



3 . . . White 000052 



,, 4 . . . Yellow . . . .000071 



5 . . . Red 000090 



The above being the reflected colours, it follows that 

 their complemontaries will be seen by transmitted light. 

 The means of measuring the length of an undulation 

 being obtained, we can next proceed to calculate their 

 peed. We have already given a table of these ;* to 

 which we now refer, whilst we enter into their calcula- 

 tion in detail. 



Having found the length, in parts of an inch, of an 

 undulation, and knowing by the eclipses of Jupiter's 

 satellites, that light travels at the rate of 192,000 miles 

 per second, in round numbers it follows that there will 

 be as many undulations of any coloured light, in a second 

 of time, as there are parts of an inch equal to the length 

 of one wave in a distance of 192,000 miles, which the 

 ray has travelled during one second. (See also p. 1G8.) 

 We have previously mentioned, t that an extreme red 

 ray lias a length of undulation of 0.0000266 of an inch ; 

 and if we divide 12165120000, the number of inches in 

 192,000 miles, by this length of one undulation, we 

 obtain the result of about 458 billions of vibrations in 

 one second of time, as producing the extreme red ray of 

 the prismatic spectrum. The same result is afforded by 

 multiplying the number of undulations per inch by the 

 number of inches in 192,000 miles. Thus : 37&10, the 

 number of undulations per inch for the red ray, multi- 

 plied by 12165120000, the number of inches in 192,000 

 miles, gives 457,898,116,800,000 as the number of undu- 

 lations per second of a ray of red light. 



AVe have been particular in detailing the mode em- 

 ployed in calculating this result, because we are not 

 aware of any work in which the entire process has yet 

 been mentioned. The student will not fail to be im- 

 pressed with the astonishing minuteness and rapidity of 

 the undulations which produce the magnificent effects of 

 colour ; and perhaps we can scarcely point out any in- 

 stance in the range of science, in which so great a number 

 of proximate causes is constantly required to produce 

 one well known, and therefore, perhaps, often unappre- 

 ciated result. 



We need scarcely add that the undulations of each of 

 the other coloured rays are calculated in a similar manner 

 for every band in the spectrum. As a matter of practice, 

 and to impress the laws which we have been here illus- 

 trating, the student will do well to continue these calcu- 

 lations of the speed of each undulation, taking the table 

 before mentioned as a guido, and as affording the requi- 

 site data. 



See antt, p. 41. + Ante, p. 41. 



