diff --git a/01.curriculum/01.physics-chemistry-biology/04.Niv4/04.electromagnetism/interferences-diffraction/interference-diffraction-main/textbook.fr.md b/01.curriculum/01.physics-chemistry-biology/04.Niv4/04.electromagnetism/interferences-diffraction/interference-diffraction-main/textbook.fr.md index 5007065a4..9d2ad5be2 100644 --- a/01.curriculum/01.physics-chemistry-biology/04.Niv4/04.electromagnetism/interferences-diffraction/interference-diffraction-main/textbook.fr.md +++ b/01.curriculum/01.physics-chemistry-biology/04.Niv4/04.electromagnetism/interferences-diffraction/interference-diffraction-main/textbook.fr.md @@ -156,9 +156,9 @@ En ces points là, *$`I_{tot}=I_{max}= 4 \,A^2`$*. Soient **N ondes** de *même amplitude $`A`$* déphasées entre-elles d'un *pas constant $`\phi`$*. -$`A_{tot}=A\,e^0\,+\,A\,e^{i\phi}\,+\,A\,e^{i\phi}\,+\,\cdot\cdot\cdot\,+\,A\,e^{i\,(N-1)\,\phi}`$ +$`A_{tot}=A\,e^0\,+\,A\,e^{i\phi}\,+\,A\,e^{i2\phi}\,+\,\cdot\cdot\cdot\,+\,A\,e^{i\,(N-1)\,\phi}`$ -$`\quad =A\,\cdot \,(1 \,+\,e^{i\phi}\,+\,e^{i\phi}\,+\,\cdot\cdot\cdot\,+\,e^{i\,(N-1)\,\phi})`$ +$`\quad =A\,\cdot \,(1 \,+\,e^{i\phi}\,+\,e^{i2\phi}\,+\,\cdot\cdot\cdot\,+\,e^{i\,(N-1)\,\phi})`$ Le *terme entre parenthèse* forment une **progression géométrique de raison $`e^{i\phi}`$**. @@ -188,7 +188,7 @@ $`\underline{A_{tot}}=A\cdot \dfrac{e^{i\,N\,\phi}-1}{e^{i\,\phi}-1}=\dfrac{(1-c L'**intensité résultante** est alors -$`I_{tot}=\underline{A_{tot}}\,\underline{A^*_{tot}}=|\,A^2\,|=A^2\cdot\dfrac{(1-cos^2\,N\phi)+sin^2\,N\phi}{(1-cos^2\,\phi)+sin^2\,\phi}`$ +$`I_{tot}=\underline{A_{tot}}\,\underline{A^*_{tot}}=|\underline{A_{tot}}^2|=A_{tot}^2=A^2\cdot\dfrac{(1-cos^2\,N\phi)+sin^2\,N\phi}{(1-cos^2\,\phi)+sin^2\,\phi}`$ $`\quad=A^2\cdot\dfrac{1-2\cos\,N\phi+cos^2\,N\phi+sin^2\,N\phi}{1-2\cos\,\phi+cos^2\,\phi+sin^2\,\phi}= A^2\cdot\dfrac{2-2\cos\,N\phi}{2-2\cos\,\phi}`$