On Immersion Ohjecfives. 213 



Deducting from this the distance C W, which is the difference 

 hetvveen the radius and thickness of the lens = "0025", we have 

 W F, the distance of the radiant from the front of the lens = • 0264", 

 as given above. 



Now in this case it is evident that the extreme ray F A forms 

 at the point A an angle of 37° with the normal to that point A C, 

 and therefore by the law of sines emerges into air at an angle of 

 66° 36' from the normal, or which is the same, 11° 24' + from 

 the optical axis. 



This is very nearly the course given to the extreme rays emerg- 

 ing from the posterior surface of the immersion lens in Mr. Wenham's 

 figure. Not exactly,. for I did not know the refractive index of his 

 front, or the exact number of degrees from the central point of its 

 posterior surface, at which the extreme rays were supposed to 

 emerge. The case, however, is a strictly parallel one, and the 

 result is accurate for the data given above. It is, however, easy to 

 show that such a front can transmit a much wider pencil from 

 balsam. In fact, it is only necessary to suppose the luminous 

 point F to be moved nearer to W, so that its new position F' shall 

 be '0168" from the anterior surface of the lens, and it will be found 

 that a pencil of 100° can be transmitted through the lens, the ex- 

 treme ray on each side emerging into the air posteriorly at the 

 point A as before, and, suffering refraction as it does so, taking the 

 course A K', which fomis an angle of 32^ 17' with the optical axis. 



For in the triangle A C F' the angle C is still 102°, and if the 

 angle F' be assumed to be 50° (the semi-aperture of the pencil sup- 

 posed to radiate from F'), the angle A will be 28°, and the side A C 

 being known, C F' is found trigonometrically to be "0193". Sub- 

 tracting C W as before, we have WF' = -0168", as stated above. 

 Also the extreme ray F' A forms an angle of 28° with the normal 

 C A, and therefore, by the law of sines, emerges at an angle of 

 45° 43' from the normal, or 32° 17' from the optical axis. If now 

 water be substituted for the balsam in front of the lens, and the 

 radiant point be moved to F", distant "0111" from the front of the 

 lens, a pencil of 122°, radiating from that j)oint to the surface of 

 the lens, will there suffer refraction and pass into the glass, the 

 extreme rays pursuing exactly the same course as in the last case, 

 and emerging into air posteriorly at the same angle, viz. 32^ 17' 

 with the optical axis. 



Of course the same reasoning will apply to balsam angles be- 

 tween 82° and 100°. For example, if with balsam in front of the 

 lens the radiant were •0218" distant, a pencil of 90° would be 

 transmitted, and the extreme ray after emerging at A would form 

 an angle of 21° 51' with the optical axis ; with water in front a 

 pencil of 107^ 38' radiating from a point "0159" distant from the 

 front of the lens would pursue the same course. 



