# Understanding Fresnel reflection coefficient formula

In textbook "Wireless Communications Principles and Practice" by Theodore S. Rappaport, the expression of Fresnel reflection coefficient ($$\Gamma$$) for parallel polarization is given as $$\Gamma_{||} = \frac{E_r}{E_i} = \frac{\eta_2 \text{sin} \theta_t- \eta_1 \text{sin} \theta_i}{\eta_2 \text{sin} \theta_t+ \eta_1 \text{sin} \theta_i}$$...(1).

However, I did not find the derivation of this eq. (1) in the same text book.

Upon checking the internet, I found the new expression of $$\Gamma$$ as

$$\Gamma_{||} = \frac{E_r}{E_i} = \frac{\eta_2 \text{cos} \theta_t- \eta_1 \text{cos} \theta_i}{\eta_2 \text{cos} \theta_t+ \eta_1 \text{cos} \theta_i}$$...(2).

I am getting doubt due to presence of "sin" and "cos" in eq. (1), (2) respectively.

My query is that are these two equations (eq.(1) and eq.(2)) same?

Any help in this regard will be highly appreciated.

• Have you checked the definitions of the angles in both references? Don't forget that $\sin x=\cos(x-\pi/2)$. Jan 30 at 11:24
• Thank u sir for ur reply... Jan 30 at 11:26