Optics Brewster's Angle Reflected Light Intesity

[frasermackay]

Homework Statement

An incident unpolarised light beam of intensity I_{0} strikes glass plate B at Brewster's Angle. The reflected light travels vertically and strikes a second glass plate A, again at Brewster's Angle. (We ignore the light transmitted by the glass plates.) Plate A is then rotated about the z-axis as shown. Briefly explain how the intensity of the light reflected by the apparatus varies with the angle of plate A. Illustrate with a qualitative sketch of intensity vs. angle of plate A.

2. The attempt at a solution

We have an unpolarised beam incident on plate B at Brewster's Angle which upon reflection should become s-polarised or polarised perpendicular to the incident plane. My understanding of Brewster's Angle then says that upon the second reflection at plate A if the plate is oriented such that the incident plane is the same as for plate B there will be no reflection. Otherwise as it rotates there will be light reflected, is this correct?

Also does the intensity of the light reflected off of A increase gradually to a maximum when the beam is parallel to the incident plane at A? Any help would be much appreciated.

 

[BvU]

No expert, but my strong feeling is that s-polarized will reflect perfectly when planes of incidence are parallel. So please check!

 

[ehild]

Homework Statement

An incident unpolarised light beam of intensity I_{0} strikes glass plate B at Brewster's Angle. The reflected light travels vertically and strikes a second glass plate A, again at Brewster's Angle. (We ignore the light transmitted by the glass plates.) Plate A is then rotated about the z-axis as shown. Briefly explain how the intensity of the light reflected by the apparatus varies with the angle of plate A. Illustrate with a qualitative sketch of intensity vs. angle of plate A.

2. The attempt at a solution

We have an unpolarised beam incident on plate B at Brewster's Angle which upon reflection should become s-polarised or polarised perpendicular to the incident plane. My understanding of Brewster's Angle then says that upon the second reflection at plate A if the plate is oriented such that the incident plane is the same as for plate B there will be no reflection. Otherwise as it rotates there will be light reflected, is this correct?

Also does the intensity of the light reflected off of A increase gradually to a maximum when the beam is parallel to the incident plane at A? Any help would be much appreciated.

Not quite ...

Unpolarised incident beam means that the beam has both p-polarized and s-polarized components with equal intensity. The parallel-polarized component does not reflect from mirror B, only the perpendicularly polarized beam travels toward A. When both mirrors align parallel the beam is reflected again.

If mirror A is turned round the vertical axis, the angle of incidence turns also. The electric field in the s- polarized beam will not be perpendicularly polarized to the plane of incidence: it will have parallel and perpendicular components. Only the perpendicular component reflects. What is the reflected intensity when mirror A is rotated by 90°?

ehild

 

[frasermackay]

Thank you very much for the help.