Introduction:
In many optical systems a series combination of two tapered plates differing in index of refraction is used as a simple beam deflector. We present here a representative set of data on the deflection caused by such a taper plate combination that was prepared with a simple MATLAB program. (The MATLAB programs are appended.) We assume that the direction of the incident light defines a reference axis and the output deviation or deflection is measured with respect to that axis. The angular deviation of each of the three planes of interest are measured with respect to the direction orthogonal to the direction of the incident light as illustrated below.Device schematic:
Definitions of terms used in this discussion:
 n_{1}: First tapered plate index of refraction
 n_{2}: Second tapered plate index of refraction
 b_{1}: First block angle
 b_{2}: Second block angle
a : Interface angleTwo particular device examples:
Device calculations:
Deflection as function of n_{2}
and b_{1}
(b_{2}=
b_{1})
with a fixed
at 30°  i.e. a slab oriented at
an angle b_{1 }wrt the direction orthogonal to the horizontal axis. 
Deflection as function of n_{2}
and b_{1}
(b_{2}=
b_{1})
with a fixed
at 30°  i.e. a slab oriented at
Note the general result that there is no deviation when the 
Deflection as function of n_{2}
and b_{1}
(b_{2}=
b_{1})
with a fixed
at 0°  i.e. a slab oriented at

Deflection as function of n_{2} and b_{2} with b_{1} and a fixed: 
MATLAB programs:
"deflection.m" the function that computes deflection by three planar surfaces
"plotit_30.m" the function that plots the data in the first graph above.
"plotit_0.m" the function that plots the data in the second graph above.
"plotit_trap.m" the function that plots the data in the third graph above.