Calculate the ratio of separation between successive (1 0 0), (11 0) and (111) lattice planes in a cubic cell.

Explanation

To calculate the ratio of separation between successive (100), (110), and (111) lattice planes in a cubic cell, we will follow these steps:

### Step 1: Understand the formula for the distance between lattice planes
The distance \( d \) between lattice planes in a cubic crystal can be calculated using the formula:
\[ d = \frac{D}{\sqrt{h^2 + k^2 + l^2}} \]
where \( D \) is the length of the unit cell (which we will assume to be 1 for simplicity), and \( (h, k, l) \) are the Miller indices of the plane.
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