#

The x-axis acts as a boundary line of two media with z equals 0. The 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 parallel components of the incident ray are E sup i x and E sup i z at H sup i and resultant vector E sup i. The parallel components of the reflected ray are E sup r x and E sup r z at H sup r and resultant vector E sup r. The parallel components of the transmitted ray are E sup t x and E sup t z at H sup t and resultant vector E sup t. The incident ray is labeled, x sub I, the reflected ray is labeled, x sub r, and the transmitted ray is labeled, x sub t.

The various components are as follows:

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

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

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

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

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

Y caret sub t equals x caret cosine of theta sub t minus z caret Sine of theta sub t. The x-axis acts as a boundary line of two media with z equals 0. The 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 parallel components of the incident ray are E sup i x and E sup i z at H sup i and resultant vector E sup i. The parallel components of the reflected ray are E sup r x and E sup r z at H sup r and resultant vector E sup r. The parallel components of the transmitted ray are E sup t x and E sup t z at H sup t and resultant vector E sup t. The incident ray is labeled, x sub I, the reflected ray is labeled, x sub r, and the transmitted ray is labeled, x sub t.

The various components are as follows:

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

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

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

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

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

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