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Dispersion

Dispersion

Jan 27, 20241 min read

  • Physics

Smaller wavelength light gets refracted more in prisms. Basically, light shone through a prism “disperses”
3b1b Video Explaining Dispersion on an atomic level with simple harmonic oscillator

n=ωck​≅2mε0​Nq2​j∑​(ωj2​−ω2)2+γj2​ω2fj​(ωj2​−ω2)​

  • Index of refraction for a medium undergoing disperision

n=1+A(1+λ2B​)


Graph View

  • n=ckω≅Nq22mε0∑jfj(ωj2−ω2)(ωj2−ω2)2+γj2ω2\displaystyle n=\frac{ck}{\omega}\cong \frac{Nq^{2}}{2m{\varepsilon}_{0}}\sum_{j} \frac{f_{j}(\omega_{j}^{2}-\omega ^{2})}{(\omega_{j}^{2}-\omega ^{2})^{2}+\gamma_{j}^{2}\omega ^{2}}n=ωck​≅2mε0​Nq2​j∑​(ωj2​−ω2)2+γj2​ω2fj​(ωj2​−ω2)​
  • n=1+A(1+Bλ2)\displaystyle n=1+A\left( 1+\frac{B}{\lambda ^{2}} \right)n=1+A(1+λ2B​)

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