Normal Shock
The jumps of the aero-thermodynamic properties of the gas across a normal shock
are derived from the conservation equations for mass, momentum and energy
(Rankine- Hugoniot).
One approximation that is commonly done is to consider the shock as an insentropic
transformation, which is a good approximation for transonic flows. With the further
approximation of ideal gas, the jumps can be cast in closed form, whose solution
is shown in the graphic below for Mach numbers M < 5.
Figure 2: Normal shock ratios at supersonic speeds
Oblique Shock
Shocks that are incident at an angle (on a wedge or similar situations) are subject
to a change of direction of the velocity in addition to the features of the normal shock.
The change of direction can be calculated with the full conservation equations, and is
found to be dependent on the density ratio shown in Fig. 2. This change occurs only in
a direction normal to the shock.
The figure below shows the oblique shock waves past a double wedge airfoil at Mach 1.8.
The visualization is a Schlieren photography.

Figure 3: Double wedge airfoil