Determinations of refractive indices in sections by the methods of Chaulnes,[33] Sorby,[34] or total reflection are accompanied by many difficulties and may fail to give satisfactory results. The Becke method, however, often furnishes a convenient means of determining the _relative_ values of the refractive indices of adjoining minerals or of minerals embedded in balsam. This is of especial service when one of the minerals is known and hence its refractive index. BECKE METHOD.[35] Suppose two adjoining minerals, in a thin rock section, to be singly refracting and to have their plane of contact vertical, _i. e._, parallel to the optic axis of the microscope. Let _A_ and _C_, Fig. 10, be two such sections with the plane of contact _OO′_ vertical, _A_ having a lower refractive index than _C_, and consider only the direction of the rays within the section, neglecting the refractive effect of the air, glass and balsam. A beam of transmitted light contains besides normal rays convergent rays, which pass through the section as indicated in Fig. 10. Consider now the cone of light rays _GBI_. The rays _O′G_ on meeting the plane of contact _OO′_ will be somewhat concentrated and deflected by the higher refractive index of _C_ and will continue as the cone _EF_. Some rays as _O′H_ will, on meeting the contact plane, be totally reflected and will continue as the cone _OE_, while the rest of the rays _HI_ will be dispersed and deflected by the weaker refractive index of _A_, continuing as the cone _OD_. Hence, more light rays will emerge on the side of the contact plane where the substance of higher refractive index lies, and there will be a concentration of illumination on this side producing the so-called “bright line.” [Illustration: FIG. 10. ]