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.

 

[paranormal]

Your understanding of Brewster's Angle is correct. When the second plate, A, is oriented such that the incident plane is the same as for plate B, there will be no reflection. This is because the light is already polarised in the same direction as the reflected light would be, so there is no need for it to be reflected again. As plate A rotates, the intensity of the reflected light will increase gradually to a maximum when the beam is parallel to the incident plane at A. This is because at this angle, the light is fully polarised and all of the incident light is reflected. A qualitative sketch of intensity vs. angle of plate A would show a gradual increase in intensity until it reaches a maximum at the angle where the beam is parallel to the incident plane, and then a decrease as the angle is further increased.