This is a question on light polarisation on a sample physics paper. Any ideas would be appreciated?

Question

Explain how linearly polarised waves need to be related to ensure that a linearly, rather than elliptically, polarised wave results from their addition. Illustrate with diagrams.How should the amplitudes of a vertically polarised wave and a horizontally polarised wave be related to ensure that a linearly polarised wave, tilted at 60degrees to the horizontal, results from their addition.

Answer 1

See Malus' Law

http://scholar.hw.ac.uk/site/physics/top...

Answer 2

First, see that the phase of the two orthogonal E-fields cross zero at the same time.

Otherwise you will get elliptical polarization, as the combined field never is zero if not both are zero at any time. Give them the same frequency.

Second, set the same wave shapes, ie sinus-formed, and let the amplitudes be the horizontal and vertical walls.

(H and V)

The vector at 60 degrees is a part, the same as a 60 degree corner triangle with all sides equal to 1.

Then, the base is half of that, which gives you the horizontal amplitude.

The height of that triangle is the vertical amplitude equal to the height of the triangle, (Phytagoras) = square-root ( (1^2-(1/2)^2) ) = sqrt (3/4) = (sqrt 3)/ 2.

So, this is for an amplitude of 1 at 60 degrees from horizontal.