Equal-width strata of a uniform cut the variance by the factor $1/L^2$

Suppose the variable Y is uniformly distributed over $(b,b+h)$. The range is divided into L strata of equal sizes. A simple random sample of size $n/L$ is selected from each stratum. If V and $V_1$ denote the variance of estimator (mean) for a simple random sample of size $n$ and a stratified random sample respectively, then: