According to IS 456: 1978, the minimum thickness of a slab required to meet the stiffness criteria is specified to ensure adequate rigidity and prevent excessive deflection under applied loads. The thickness is governed by the span of the slab, denoted by \( L \), with the short span of the slab being the determining factor.
As per the code, the minimum total thickness of a slab should not be less than \( \frac{L}{35} \), where \( L \) is the short span of the slab. This requirement is intended to ensure that the slab has sufficient stiffness to limit deflections within acceptable limits.
\[
\text{Minimum thickness of slab} = \frac{L}{35}
\]
This ensures that the slab is stiff enough to carry the loads and also meet the deflection limits specified by IS 456. The other options, such as \( \frac{L}{15} \), \( \frac{L}{45} \), and \( \frac{L}{25} \), do not conform to the standard, as these values are not the minimum thickness prescribed for the slab’s stiffness.
Therefore, the correct answer is \( \frac{L}{35} \).