Fringes for Internal Reflexion, 507 



accurately by scattering a little dust — lycopodium powder — 

 on the surface. If the part of the surface seen in the 

 microscope be illuminated, these specks of dust and their 

 images in the surface can be easily seen. They and the 

 images form a symmetrical figure, and the line of symmetry 

 determines the surface very accurately. For photographing 

 the fringes a brass tube was fitted to an ordinary camera 

 and the lens placed at the end of the tube, a distance of about 

 120 cm. being thus secured between the lens and the plate. 

 Fringes formed in the trough at the appropriate distance 

 were thus automatically focussed on the plate and an exposure 

 was made. The photographs 1 and 2 in Plate XIII. were ob- 

 tained in this way. In the photographs the surface is not 

 very definitely shown, as the specks of dust were continually 

 moving, and long exposures had to be given to obtain the 

 fringes. The photographs 3 and 4 are of Lloyd's fringes, 

 obtained in a similar way with a single mirror of black glass. 

 These are given for comparison. It is clear that the two sets 

 of fringes are of the same type, and indicate that in each case 

 there is the loss of half an undulation on reflexion. 



The use of polarized light made no difference to the/fringes, 

 so that whatever be the plane of polarization foi/ grazing 

 incidence there is a loss of half an undulation. 



The width of the fringes can easily be altered by adjusting 

 the position of the slit. The glass ends of the trough make 

 no difference to the fringes, as the direct and reflected pencils 

 both pass through the same glass path, so that, provided the 

 glass is fairly good, clear fringes are obtained. 



If we now consider the Fresnel formulae for the changes 

 of phase on reflexion in conjunction with the Stokes proposi- 

 tion concerning amplitudes we can see that these results are 

 in agreement with the results for external reflexion. We 

 have two cases to consider : — Light polarized in the plane of 

 incidence and light polarized perpendicularly to this plane. 

 Let the angle of incidence be </>, then for incidence at an 

 angle greater than the critical angle a, we have in each type 

 of light a change of phase on reflexion. Let y t and y p be the 

 changes of phase for light polarized in and perpendicular to 

 the plain of incidence respectively. Then 



tan Yi = 2cos< ft Vsin 2 <ft — sin 2 a 

 cos 2 <p -f sin 2 a. 



2 cos <f> sin 2 a\ / sin 2 d> — sin 2 « 



tan 7p = . 4 v . J . ■ 



cos J <£ sin a — sin" 1 (j> + snra 



