What is the cross between the progeny of $F_1$ and the homozygous recessive parent called ? How is it useful ?

Mendel self-pollinated the $F_2$ plants and found that dwarf $F_2$ plants continued to generate dwarf plants in $F_3$ and $F_4$ generations. He concluded that the genotype of the dwarfs was homozygous -$tt$. 

it is clear that though the genotypic ratios can be calculated using mathematical probability, but simply looking at the phenotype of a dominant trait, it is not possible to know the genotypic composition.

That is, for example, whether a tall plant from $F_1$ or $F_2$ has $TT$ or $Tt$ composition, cannot be predicted. Therefore, to determine the genotype of a tall plant at $F_2$, Mendel crossed the tall plant from $F_2$ with a dwarf plant. This he called a test cross.