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The horizontal axis represents the z-axis and the vertical axis represents the x-axis. The x-axis acts as a boundary line of two media with z equals 0. An incident ray travels below the negative z-axis from the medium 1 (epsilon sub 1, micro sub 1) to the origin with incident angle theta sub I and reflects back to the medium 1 above the negative z-axis with reflected angle theta sub r. The wave partially transmitted in the medium 2 above the z-axis with an angle theta sub t.

The perpendicular components of the incident ray are H sup i x and H sup i z at E sup i and resultant vector H sup i. The perpendicular components of the reflected ray are H sup r x and H sup r z at E sup r and resultant vector H sup r. The perpendicular components of the transmitted ray are H sup t x and H sup t z at E sup t and resultant vector H sup t. The incident ray is x sub I, the reflected is ray x sub r, and the transmitted ray is x sub t. A ray x sub i is above the transmitted ray. The enlarged view of x sub t is labeled Inset C, An x z plane with a ray x sub t rising steeply, in the first quadrant with angle theta sub t. The enlarged view of x sub r is labeled Inset B, An x negative z plane with a ray x sub r rising steeply, in the second quadrant with angle theta sub r. The enlarged view of x sub i is labeled Inset A, An x z plane with a ray x sub t rising steeply, in the first quadrant with angle theta sub i. Unit vectors of the incident, reflected, and the transmitted rays are K sub I caret, K sub r caret, and K sub t caret respectively.

The various components are as follows:

Y caret sub r equals x caret cosine of theta sub r plus z caret Sine of theta sub r.

Y caret sub i equals negative x caret cosine of theta sub i plus z caret Sine of theta sub i.

Y caret sub t equals negative x caret cosine of theta sub t plus z caret Sine of theta sub t.

X sub t equals x sine of theta sub t plus z cosine of theta sub t.

X sub r equals x sine of theta sub r minus z cosine of theta sub r.

X sub I equals x sine of theta sub I plus z cosine of theta sub i.