FLP: Derivation of reflection coefficient

[duffing]

In Vol. I Ch.33 of Feynman's Lectures (http://www.feynmanlectures.caltech.edu/I_33.html), 33-6, the reflection coefficient as a function of angle was derived.

I am confused about the part where it said the component of A perpendicular to B (Acos (i+r)) has the right polarisation to produce B. Geometrically I obtained Asin(i+r) instead but I am unsure about why the physics is so.

Similarly, it was also mentioned that the component of A normal to the dashed line (Acos(i-r)) is effective in producing the field of magnitude -1. I am confused as to why this component produces the field of magnitude -1.

Thanks.

 

[pixel]

I am confused about the part where it said the component of A perpendicular to B (Acos (i+r)) has the right polarisation to produce B. Geometrically I obtained Asin(i+r) instead but I am unsure about why the physics is so.

If you're asking about the physics rather than the specific formula, the electric field vector is always perpendicular to the direction of the ray. The component of A parallel to B cannot contribute to light in the B direction.