= Solution
The lamellar interfaces now make $60^\circ$ with the surface normal, or $30^\circ$ with the surface itself. \b[Draw inclined alternating plates rather than vertical stripes], with preferentially etched <ferrite> below the more resistant <cementite>.
\Image[/past-exam-of-the-materials-science-course-of-the-university-of-cambridge/2018/paper-1-pearlite.png]
{title=Original inclined-lamella etching geometry and illustrative AFM profile; the synthetic spacing and fractions are not a tracing of the source data}
The upper panel shows an inclined microstructure intersecting the original plane. Differential etching can expose a shallow inclined <cementite> face on one side of a ridge and an undercut or overhang on the other. The lower panel shows its accessible height profile, with additional rounding from a finite tip. It is therefore possible to obtain an asymmetric ridge even from an initially planar section through parallel lamellae.
For an ideal unetched planar cut, a plate of normal thickness $d$ has apparent surface width
$$
w=\frac{d}{\sin30^\circ}=2d.
$$
The same factor applies to the <ferrite> spacing. Inclination alone broadens all intersections together; it does not by itself change the true phase-width ratio.
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