324 Prof. A. Kundt on the Electromagnetic Rotation 



VII. 



Rotation of the Plane of Polarization of Light which has twice 

 traversed a glass plate and been reflected at the back sur- 

 face of the plate. 



The phenomena of reflection of light from metals have led 

 to the view that the light upon reflection penetrates into the 

 metal to a certain depth. This easily suggests the suspicion 

 that the rotation of the plane of polarization of light which 

 has suffered reflection from magnetic metallic surfaces arises 

 in the very thin layer which the rays traverse upon reflection. 

 A theory of rotation upon the assumption of the penetration 

 of the light would be difficult to establish. 



We may, however, easily state matters so that, in general 

 at least, a process takes place analogous to that of reflection at 

 metallic surfaces, upon the assumption of the penetration of 

 light. Suppose that we have a glass plate in a magnetic 

 field : let rays of light fall upon it at any angle of incidence. 

 The rays are refracted into the glass, traverse the plate, are 

 reflected at the back surface, and after traversing the plate a 

 second time are refracted out of the glass. 



If we have the amount of the electromagnetic rotation of 

 the rays by glass given, then, by help of Fresnel's formula 

 for reflection and refraction in isotropic bodies, the total rota- 

 tion which the plane of polarization has suffered in the plate 

 can be calculated. We will consider the following special 

 case, which is analogous to our previous experiments on rota- 

 tion at the side-faces of a magnet. 



Let the lines of force of the magnetic field in which the 

 glass plate is placed be parallel to the plane of the plate. Let 

 the thickness of the plate be d, and the electromagnetic rota- 

 tion per unit length in the direction of the lines of force be (f>. 

 Let the plane of polarization of the incident light coincide with 

 the plane of incidence, and be parallel to the lines of force. 

 Then, if Fresnel's formula for refraction at the first surface 

 and reflection at the second surface be employed, the angle 7 

 through which the plane of polarization is rotated upon emer- 

 gence from the plate — if i and r represent the angles of inci- 

 dence and refraction, and if the electromagnetic rotation in 

 the plate is so small that the angle, its tangent, and its sine 

 may be considered identical — is given by the formula 



sin i sin r 

 tan 7 = 2^tan 7 - os2( ._ r y 



Since all the factors of </> are positive, 7 has the same sign as 

 </> for any value of i. For i — 0, 7 = 0. The rotation of the 



