  A cosmological observable measured in a range of redshifts can be used as a
probe of a set of cosmological parameters. Given the cosmological observable
and the cosmological parameter, there is an optimum range of redshifts where
the observable can constrain the parameter in the most effective manner. For
other redshift ranges the observable values may be degenerate with respect to
the cosmological parameter values and thus inefficient in constraining the
given parameter. These are blind redshift ranges. We determine the optimum and
the blind redshift ranges of cosmological observables with respect to the
cosmological parameters: matter density parameter $\Omega_m$, equation of state
parameter $w$ and a modified gravity parameter $g_a$ which parametrizes the
evolution of an effective Newton's constant. We consider the observables:
growth rate of matter density perturbations expressed through $f(z)$ and
$f\sigma_8$, the distance modulus $\mu(z)$, Baryon Acoustic Oscillation
observables $D_V(z) \times \frac{r_s^{fid}}{r_s}$, $H \times
\frac{r_s}{r_s^{fid}}$ and $D_A \times \frac{r_s^{fid}}{r_s}$, $H(z)$
measurements and the gravitational wave luminosity distance. We introduce a new
statistic $S_P^O(z)\equiv \frac{\Delta O}{\Delta P}(z) \cdot V_{eff}^{1/2}$,
including the effective survey volume $V_{eff}$, as a measure of the
constraining power of a given observable $O$ with respect to a cosmological
parameter $P$ as a function of redshift $z$. We find blind redshift spots $z_b$
($S_P^O(z_b)\simeq 0$) and optimal redshift spots $z_s$ ($S_P^O(z_s)\simeq
max$) for these observables with respect to the parameters $\Omega_m$, $w$ and
$g_a$. For $O=f\sigma_8$ and $P=(\Omega_{m},w,g_a)$ we find blind spots at
$z_b\simeq(1,2,2.7)$ respectively and optimal (sweet) spots at
$z_s=(0.5,0.8,1.2)$. Thus probing higher redshifts may be less effective than
probing lower redshifts with higher accuracy.
