Question

A plane intersects the coordinate axes at \(x = \frac{2}{3},\;y = \frac{1}{3}\;and\;z = \frac{1}{2}\) what is the Miller index of this plane?
1. 9,3,2
2. 4,3,2
3. 4,2,3
4. 3,6,4

Answer 1

Correct Answer - Option 4 : 3,6,4

Explanation:

Miller indices are rationalized reciprocal of fractional intercepts taken along the crystallographic directions.

Calculation:

Given: 

Plane intercepts are \(x = \frac{2}{3},y = \frac{1}{3}and\;z = \frac{1}{2}\)

Plane ABCD	x	y	Z
Intercept	\(x = \frac{2}{3}\)	\(x = \frac{1}{3}\)	\(x = \frac{1}{2}\)
Reciprocal	\(\frac{3}{{2}}\)	\(\frac{3}{1 }\)	\(\frac{2}{1 }\)
Rationalization	\(x = \frac{3}{2}\times2=3\)	\(x = \frac{3}{1}\times2=6\)	\(x = \frac{2}{1}\times2=4\)
Indices	3	6	4

∴ Miller index of this plane will be 3,6,4