Miller Indices of a Plane Parallel to the x-axis with Intercepts of 2 and ½ along the y and z-axis

To determine the Miller indices of a plane that is parallel to the x-axis and cuts intercepts of 2 and ½ along the y-axis and z-axis, we can use the following steps:

Step 1: Determine the intercepts
The intercepts of the plane along the y-axis and z-axis are given as 2 and ½ respectively.

Step 2: Convert the intercepts to fractional intercepts
To convert the intercepts to fractional intercepts, we need to find the reciprocals of the intercepts. The reciprocal of 2 is 1/2 and the reciprocal of ½ is 2.

Step 3: Find the lowest common multiple (LCM)
Next, we need to find the lowest common multiple (LCM) of the fractional intercepts. The LCM of 1/2 and 2 is 2. Therefore, the LCM is 2.

Step 4: Determine the Miller indices
The Miller indices of a plane are denoted by (hkl), where h, k, and l are integers. To determine the Miller indices, we divide the LCM by the fractional intercepts.

In this case, the Miller indices can be calculated as follows:
- The Miller index h is obtained by dividing the LCM (2) by the fractional intercept along the x-axis (1), which gives h = 2/1 = 2.
- The Miller index k is obtained by dividing the LCM (2) by the fractional intercept along the y-axis (1/2), which gives k = 2/(1/2) = 2 * 2 = 4.
- The Miller index l is obtained by dividing the LCM (2) by the fractional intercept along the z-axis (2), which gives l = 2/2 = 1.

Therefore, the Miller indices of the plane parallel to the x-axis and cuts intercepts of 2 and ½ along the y-axis and z-axis are (2 4 1).