## CENTRED ACUTE BISECTRIX

In a centred acute bisectrix figure two rays of light propagate along the acute bisectrix which is either the X or Z indicatrix axis, and emerge in the centre of the Bxa interference figure, which is the point where the two isogyres cross.

At extinction the two rays vibrate parallel to the upper and lower polarizers forming the centre of cross.

1. One ray vibrates parallel to the Y indicatrix axis and has an index of refraction equal to nbeta.
This ray orientation is also parallel to the optic normal, the Y indicatrix axis, and corresponds to the fatter arm of cross.
2. The other ray vibrates parallel to the obtuse bisectrix of the indicatrix and has an index of refraction equal to nBxo.
This ray vibration direction is also parallel to the optic plane and corresponds to the thinner arm of cross. The optic plane contains the Bxa, Bxo and the melatopes.

For optically positive minerals, the obtuse bisectrix is the X axis and nBxo = nalpha, and corresponds to the fast ray, remember that (nalpha < nbeta < ngamma).

For optically negative minerals, obtuse bisectrix is the Z axis and nBxo = ngamma, and corresponds to the slow ray.

Must determine whether the ray vibrating parallel to the obtuse bisectrix is the fast or slow ray.

To determine whether the X or Z axis is the acute bisectrix, and therfore whether the mineral is optically negative or positive, the interference figure must be rotated such that the optic plane is oriented NE-SW.

The steps to follow to determine the optic sign are:

1. #### Obtain an acute bisectrix interference figure.

Rotate the stage so that the trace of the optic plane is oriented NE-SW, i.e., the isogyre cross will split and move into the NE and SW quadrants.
• if 2V angle is small, < ~40°, both isogyres will be visible in field of view.
• if 2V angle is large, > ~40°, the isogyres will lie outside the field of view.
2. #### Insert accessory plate.

With the interference figure in the 45° position, the optic plane is oriented NE-SW, such that it is parallel with the slow vibration direction of the accessory plate. Observe the colour change that results.
3. #### Interpretation.

If the interference colours between the melatopes decrease the ray vibrating parallel to Bxo (parallel to optic plane) must be the fast ray so Bxo = X axis (X = fast ray) and Bxa, which is vertical, = Z axis. The mineral is optically positive.

If the interference colours between the melatopes increase, the ray vibrating parallel to Bxo must be the slow ray, so Bxo = Z axis, and Bxa = X axis. The mineral is optically negative.

If the trace of the optic plane is placed such that it lies in the NW-SE, the areas of addition and subtraction observed for the interference colours will be reversed.

If the interference figure displays few to no isochromes use the gypsum plate to determine the optic sign.

With the gypsum plate inserted the area between the isogyres will exhibit either:

1. A decrease in colours, from white to yellow, (shown on the left above) indicates that the vibration direction in the interference figure, which is parallel to the optic plane is the FAST RAY. This colour change tells us that the ray which is vibrating parallel to the optic plane has a low index of refraction and must correspond to nalpha as measured along the X indicatrix axis. Therefore the Z indicatrix axis must be the Bxa.
2. An increase in colours, from white to blue, (shown on the right above) indicates that the vibration direction in the interference figure, which is parallel to the optic plane is the SLOW RAY. This colour change tells us that the ray which is vibrating parallel to the optic plane has a high index of refraction and must correspond to ngamma as measured along the Z indicatrix axis. Therefore the X indicatrix axis must be the Bxa.

If there are numerous isochromes use the quartz wedge and watch the directions in which the isochromes move with respect to the isogyres, as the wedge is inserted.

With insertion of the quartz wedge into the light path, the isochromes will move.

1. Where colours increase, i.e. where the slow ray of the mineral is parallel with the slow ray of the wedge, the isochromes will move into the figure towards the melatopes, to be replaced by higher order colours from the edge of the figure.
2. Where the colours decrease, i.e. where the fast ray of the mineral is parallel with the slow ray of the wedge, the isochromes will move out of the figure away from the melatopes, to be replaced by lower order colours.