# Reflection coefficient derivation

from fresnel equations we have

$$r_{parallel}=\frac{n_1\cos\theta_i-n_2\cos\theta_r}{n_1\cos\theta_i+n_2\cos\theta_r}$$ $$r_{perpendicular}=\frac{n_2\cos\theta_i-n_1\cos\theta_r}{n_1\cos\theta_i+n_2\cos\theta_r}$$

reflection coefficient

$$R=r_{parallel}^2+r_{perpendicular}^2$$

am I right? I don't know, cannot find any information anywhere, just guessing. Alright, therefore

$$R=2\cdot(\frac{n_2-n_1}{n_2+n_1})^2$$

but apparently the correct answer is

$$R=(\frac{n_2-n_1}{n_2+n_1})^2$$

I am not sure if that is correct answer either; it is written a lot all over the internet so I guess it is.

These two formulae are not the same, why the result I am getting is different? Need an explanation

$$R = \frac{1}{2}(r_{parallel}^2+ r_{perpendicular}^2)$$
$$\theta_i = \theta_r = 0$$