The Miller index for the plane as shown in the figure and parallel to the c-axis, is

Concept:

→ The Miller index notation is a system used to describe the orientation of crystal planes in a lattice.

→ The notation consists of three integer numbers enclosed in square brackets [h k l], known as Miller indices, which represent the reciprocal intercepts of the plane with the crystallographic axes.

Explanation:

b represents y- axis and a represents x-axis and c parallel to this is y-axis, the miller index corresponding to c-axis will be infinity.

→ In the figure, the plane intersects the a-axis at 4 unit, the b-axis at 2 units, and is parallel to the c-axis which is at 0 unit.

→ Intercept value along a, b and c axes are (4, 2, \(\propto \))

→ Now, take the reciprocal of these intercepts:

\(\frac{1}{4},\frac{1}{2},\frac{1}{\propto }\) ⇒ \(\frac{1}{4},\frac{1}{2},0\)

Multiply all of these with highest integer i.e., 4 we will get

[1,2,0]

→ This notation indicates that the plane is perpendicular to the c-axis and contains the direction of the vector [1, 2, 0] in the crystal lattice.

Conclusion:
The correct answer is option 2.