** Amplitude reflection and transmission coefficients for perpendicular polari-sation**

**Figure: EM field geometry for perpendicular (σ, s) polarisation. The electric field is shown pointing out of the page.**

The EM field geometry for perpendicular (σ, s) polarisation is shown in Figure. In this case, E • e_{1} = 0, E • e_{3} = 0 and B • e_{2} = 0, and so the three simultaneous equations remaining are

Solving simultaneous Equations we obtain;

Using Snell’s law **n _{t} sin θ_{t} = n_{i} sin θ_{i}** from which;

**cos θ _{t} = √ (1 – n_{i}^{2} / n_{t}^{2} sin^{2} θ_{i})**

we arrive at the amplitude reflection coefficient for perpendicular polarisation,

and the amplitude transmission coefficient for perpendicular polarisation,