An optical filter can be described by a Jones matrix

Obtain the form of the emerging light for each of the following incident beams:
(a) A plane polarized beam polarized at angle θ to the horizontal (see Problem 8.75).

(b) A left-circularly polarized beam.
(c) A right-circularly polarized beam.
Data from Prob. 8.75

The Jones vector for an arbitrary linearly polarized state at an angle θ with respect to the horizontal is

Prove that this matrix is in agreement with the one in Table 8.5 for a P-state at +45°.

Table 8.5

sin a cos a -sina cos. [cose sin 0