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5.3: Interference of Monochromatic Fields of the Same Frequency
https://phys.libretexts.org/Bookshelves/Optics/BSc_Optics_(Konijnenberg_Adam_and_Urbach)/05%3A_Interference_and_coherence/5.03%3A_Interference_of_Monochromatic_Fields_of_the_Same_Frequency
Hence we define $I_{1}=\left|U_{1}\right|^{2}$ and $I_{2}=\left|U_{2}\right|^{2}$ , and we then find for the time-averaged intensity of the sum of $U_{1}$ and $U_{2}$ : \[\begin{aligned} I &=\l...Hence we define $I_{1}=\left|U_{1}\right|^{2}$ and $I_{2}=\left|U_{2}\right|^{2}$ , and we then find for the time-averaged intensity of the sum of $U_{1}$ and $U_{2}$ : $\begin{aligned} I &=\left|U_{1}+U_{2}\right|^{2}=\left(U_{1}+U_{2}\right)^{*}\left(U_{1}+U_{2}\right) \\ &=\left|U_{1}\right|^{2}+\left|U_{2}\right|^{2}+U_{1}^{*} U_{2}+U_{1} U_{2}^{*} \\ &=I_{1}+I_{2}+2 \operatorname{Re}\left[U_{1}^{*} U_{2}\right]. \end{aligned} \nonumber$

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