When will electromagnetic waves reflect? What are the criteria for reflections?
Yea dependence is there.

At the interface between two mediums : 1 and 2, the amount of reflection of EM waves for perpendicular incidence, can be described by its reflection coefficient. 
$$\rho = \left(\frac{\eta_1 -\eta_2}{\eta_1 +\eta_2}\right)$$
where,
$$\eta_1 = \sqrt{\mu_1/\epsilon_1}$$
$$\eta_2 = \sqrt{\mu_2/\epsilon_2}$$
similarly the amount of transmission can be described corresponding transmission coefficient
$$\tau = 1+\rho $$

EDIT: 

The coefficients are defined in terms of amplitudes of the incident, transmitted and reflected waves.