Consider that the vibration of polarisation is along OP. On passing through the glass half the vibrations remain along OP. But on passing through quartz half these vibrations will split into 0- and £-components. The £-components are parallel to the optic axis while O- component is perpendicular to optic axis. The O-component travels faster in quartz and hence an emergence 0-component will be along OD instead of along OC. Thus components OA and OD will combine to form a resultant vibration along OQ which makes same angle with optic axis as OP. Now if the Principal plane of the analyzing Nicol is parallel to OP then the light will pass through glass half unobstructed. Hence glass half will be brighter than quartz half or we can say that glass half will be bright and the quartz half will be dark. Similarly if principal plane of analyzing Nicol is parallel to OQ then quartz half will be bright and glass half will be dark.