The accessory plates allow for the determination of the FAST (low n) and SLOW (high n) rays which exit from the mineral being examined.
The plates consist of pieces of quartz, gypsum or muscovite mounted in a holder so that the vibration directions of the mineral piece are parallel to the long and short axis of the holder.
Consider a mineral grain lying on the stage such that its vibration directions are in the 45° position.
The light passing through the mineral is split into two rays, with the slow ray retarded behind the fast ray upon exiting the grain, retardation = D1.
The accessory plate, gypsum plate, has a constant thickness and therefore a constant retardation, DA.
If the accessory plate is superimposed over the mineral so that the slow ray vibration directions are parallel, then the ray that is the slow ray exiting the mineral is the slow ray in the accessory plate and it is further retarded.
The result is a higher total retardation
D1 + DA = D2
The two rays when they reach the upper polar result in a higher order of interference colour, the total retardation is higher and lies to the right of the original colour on the interference colour chart.
Rotating the mineral 90° results in the fast ray vibration direction of the mineral being parallel to the slow ray vibration direction of the accessory plate.
The ray which was the slow ray in the mineral becomes the fast ray in the accessory plate.
The result is that the accessory plate cancels some of the retardation produced by the mineral, the total retardation:
D1 - DA = D3
The interference colour produced at the upper polar is a lower order colour.
All accessory plates used are constructed such that the slow vibration direction is across the width of the plate, the fast vibrations direction is parallel to the length.
Accessory Plates are inserted into the microscope between the objective lens and the upper polar, in the 45° position.