Notes. 571 



position of the second grating, but solely on the angles C B V and C B R. Means 

 are therefore at hand — 



1. To obtain parallel rays of light of different colours, spaced in accordance 

 with their wave-length, precisely as occurs in the back focal plane of the 

 objective proper, in the Demonstration Microscope, where the diffraction is 

 caused by the object-grating itself. 



2. To vary the width between the central ray and the diffracted ray of 

 any order, without disturbing the parallelism of any of the rays, so that this 

 width can be made the same as if the rays had been diffracted by the object. 



That the dioptric and diffracted rays of any one colour will be capable of 

 interference in the one case, just as in the other, is obvious, for in both cases 

 they have been derived from the same source. 



But two points of difference should be noticed — 



1. In the case of the Microscope the relative intensity of the dioptric and 

 the diffracted beams in the back focal plane of the Microscope depends upon 

 the pitch of the o&/ec£-grating. 



In the method under consideration not only do the relative intensities of 

 the dioptric and diffracted beams depend upon the pitch of the particular 

 gratings used, but they vary in quite a different ratio. For, suppose for a 

 moment that the violet ray impinging on the first grating has an intensity 

 100, and that the relative intensity of the dioptric and diffracted ray of the 

 first order is as 50 to 20 when it has passed the first grating, then, when the 

 rays pass the second grating, the components of the same, parallel to the in- 

 cident ray have a relative intensity of 25 to 4. This is seen on reference to 

 fig. 137, in which the intensities of the rays are written alongside. It is 

 evident that the parallel components emerging from the second lens arc 

 diminished in intensity, according to the square of the rate at which they 

 are diminished on emergence from the first grating. 



2. In the Microscope the diffracted and the dioptric rays from an object 

 point on the axis of the instrument arrive in the back focal plane in the 

 same phase, because the optical path-length is the same. In the double- 

 grating method the phase differs according to the difference in the path- 

 length between B C and B V (fig. 136), which varies according to the distance 

 between the gratings. 



These two points of difference are got rid of by utilising in both instances 

 only the two diffraction bands of the first order, i.e. the one on the left and 

 the one on the right of the central beam. The central beam itself is blocked 

 out by means of a stop placed between H H 1 and T T (not shown in fig. 134). 



The result of the experiment * was that a grating structure with perfectly 

 sharp black and white lines was seen exactly as if it had proceeded from the 

 object grating in the ordinary way, so that it seemed at first as though Abbe's 

 laws referred to above had been circumvented. But the idea was easily 

 dispelled, as the appearance of structure remained just as before, on rotating 

 the object-grating on the stage, and it was then found that it remained when 

 the object-grating was removed altogether. 



So far as the Microscope image was concerned, these experiments had a 

 negative result: they had merely been an object-lesson as to the correct- 

 ness of Abbe's laws as to resolving power and the nature of the image, 

 inasmuch as they showed what difficulties beset the path of an attempt at 

 evading them, even in so artificial a manner as the one described. Tin \ had 

 led, however, to a simple way of producing achromatic interference hands 

 which might be termed the "double grating method," and which the author 

 was hopeful might be found of practical utility in other directions, in view 

 of the convenience of being able to use white instead of homogeneous light 

 and of the facility with which the spacing of the bands could be varied. 



* Dftailed particulars are given in the paper of the apparatus, the method of 

 performing the experiment, and the precautions necessary to avoid failure. 



