The Miller indices of the planes parallel to the b axis and intersecting the a and c axis, as shown in the figure, are

Concept:

• Miller Indices are imaginary mathematical representation. 
• It represents the set of parallel crystallographic planes passing using the numeric values (h, k, l)
• If the intercept of the plane at imaginary three coordinate axes is known, miller indices can be calculated by simply taking the reciprocal of intercept values and converting them to integers.
• In Miller Index notation, if a plane has 0 value with respect to certain axis, it means it is parallel to that axis.

Explanation.

The given planes are parallel to b-axis, that means the miller index corresponding to b-axis will be 0.

To get the miller indices values for other two axes, first define an origin for different planes and find the intercept values.

For plane (i)

Intercept value along a, b and c axes are (2, 0, 2)

Corresponding Miller Indices value is

= \((\frac{1}{2}0 \frac{1}{2}) \)  

= \((101)\) 

For plane (ii)

Intercept value along a, b and c axes are (4, 0, 2)

Corresponding Miller Indices value is 

= \((\frac{1}{4}0 \frac{1}{2}) \)  

= \((102)\)                

Conclusion:

Hence, the Miller indices of the planes parallel to the b axis and intersecting the a and c axis as given are (i) 101, (ii) 102