Reciprocal lattice is a concept used in solid state physics to describe the periodicity of a crystal lattice in reciprocal space. It is a mathematical construct that provides a convenient way to analyze the diffraction patterns produced by crystals.

The reciprocal lattice is derived from the direct lattice, which represents the arrangement of atoms in the crystal. In the case of a simple cubic lattice, the direct lattice consists of an infinite array of points arranged in a simple cubic structure, with lattice points located at the corners of the unit cell.

To determine the reciprocal lattice for a given direct lattice, we need to define a set of reciprocal lattice vectors. These vectors are chosen such that their dot products with the direct lattice vectors are all integers.

In the case of a simple cubic lattice, the direct lattice vectors are given by:

a1 = a * x̂
a2 = a * ȳ̂
a3 = a * ẑ

where a is the lattice constant and x̂, ȳ̂, and ẑ are the unit vectors along the x, y, and z axes, respectively.

To find the reciprocal lattice vectors, we use the formula:

b1 = 2π(a2 × a3) / (a1 · (a2 × a3))
b2 = 2π(a3 × a1) / (a1 · (a2 × a3))
b3 = 2π(a1 × a2) / (a1 · (a2 × a3))

where × denotes the cross product and · denotes the dot product.

In the case of a simple cubic lattice, the reciprocal lattice vectors are given by:

b1 = 2πȳ̂ × ẑ / (a^3)
b2 = 2πẑ × x̂ / (a^3)
b3 = 2πx̂ × ȳ̂ / (a^3)

These reciprocal lattice vectors represent the periodicity of the simple cubic lattice in reciprocal space. The reciprocal lattice itself is also a simple cubic lattice, with lattice points located at the corners of the unit cell. Therefore, the correct answer is option B - simple cubic.