Abstract: By using the electric vector expressions of electromagnetic waves after reflection and refraction at the boundary surface of two types media, the article gets a mathematics expression to explain quantitatively the pha- sic variation of electric vector before and after reflecting. According to the Brewster angle, the phasic variation of the reflected wave and incident wave of electric vector for differently incident angles are discussed. Considering the menbrane of silicon dioxide as an example, the index of refraction vary with wavelengths and the variation trend of the wave path-difference are discussed under different wavelengths of electromagnetic waves entering membrane from air.

Key words: electromagnetic wave, Fresnel formula, Brewster angle, mathematical expression, half-wave loss