Question

A mineral has X = c, Y = b, Z = a, where X, Y, Z denote optical directions and a, b, c denote crystallographic axes. If X is the fast vibration direction and the mineral is optically positive, a {001} section will show which one of the following interference figures?

• A. Obtuse bisectrix
• B. Acute bisectrix
• C. Centered uniaxial
• D. Off-centered uniaxial

Hint:

Find which principal direction is the obtuse bisectrix for a positive mineral, then check what direction the {001} section is viewed along.

Answer 1

The Correct Option is A

Step 1: Identify the optical orientation of the mineral.
We are told \(X=c\), \(Y=b\), \(Z=a\), which means the three principal vibration directions of the indicatrix, \(X\), \(Y\) and \(Z\), coincide exactly with the crystallographic axes \(c\), \(b\) and \(a\) respectively. This kind of orientation, where the optical directions line up with the crystallographic axes, is typical of an orthorhombic biaxial mineral.

Step 2: Recall the meaning of acute and obtuse bisectrix for a positive mineral.
In a biaxial mineral, the two optic axes lie in the plane containing \(X\) and \(Z\), called the optic axial plane. The vibration direction that bisects the sharp (acute) angle between the two optic axes is called the acute bisectrix, written \(Bx_a\), and the direction bisecting the wide (obtuse) angle is the obtuse bisectrix, written \(Bx_o\). For an optically positive mineral, \(Z\) is the acute bisectrix and \(X\) is the obtuse bisectrix. For an optically negative mineral it is the other way round, \(X\) is acute and \(Z\) is obtuse.

Step 3: Apply this rule to our mineral.
We are told the mineral is optically positive, so by the rule in Step 2, \(Z\) is the acute bisectrix and \(X\) is the obtuse bisectrix. Since \(X=c\) from Step 1, the crystallographic \(c\)-axis is the obtuse bisectrix direction of this mineral.

Step 4: Work out the viewing direction for a \(\{001\}\) section.
A \(\{001\}\) section is a crystal face, or a thin section cut, that is perpendicular to the \(c\)-axis. Looking through such a section means the microscope is viewing straight down the \(c\)-axis, which we have identified as \(X\), the obtuse bisectrix direction.

Step 5: Recall what interference figure appears when viewing down a bisectrix.
When a biaxial mineral is viewed with the microscope axis lined up along one of its principal optical directions \(X\), \(Y\) or \(Z\), and that direction is one of the two bisectrices, the conoscopic interference figure obtained is centred and shows the pair of melatopes symmetrically placed about the centre, forming a bisectrix figure. Since the viewing direction here is \(X\), the obtuse bisectrix, the figure produced is specifically the obtuse bisectrix figure.

Step 6: Eliminate the other options.
An acute bisectrix figure would appear only if we viewed down \(Z\), not \(X\), so option (B) does not apply here. A centred or off-centred uniaxial figure belongs to uniaxial minerals with a single optic axis, not to this biaxial mineral with \(X\), \(Y\), \(Z\) all distinct, so options (C) and (D) do not apply either.

Step 7: Final conclusion.
Therefore, the \(\{001\}\) section of this optically positive mineral shows the
\[ \boxed{\text{Obtuse bisectrix figure}} \]