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An optical fiber consists of a cylindrical dielectric rod of refractive index $\mathrm{n}^{1}$, surrounded by another dielectric of refractive index $n^{2}$, where $n^{2} < n^{1},$ as shown in the following figure. If a ray is incident from air at an angle $i$ to the axis, then it undergoes total internal reflection at the interface $AB$ if

  1. $i \geq \sin ^{-1} \sqrt{n_{1}^{2}-n_{2}^{2}}$
  2. $i<\sin ^{-1} \sqrt{n_{1}-n_{2}}$
  3. $i \geq \sin ^{-1} \sqrt{n_{1}^{2}-n_{2}^{2}}$
  4. $i=\sin ^{-1} \sqrt{n_{1}-n_{2}}$

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