Question

Fiber optics are an important part of our modern internet. In these fibers, two different glasses are used to confine the light by total internal reflection at the critical angle for the interface between the core (ncore =1.497) and the cladding (ncladding =1.421)

Answer 1

Complete Question

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Answer:

a

$\theta_{max} =18.38^o$

b

New  $n_{cladding} =1.491$

Explanation:

 From the question we are told that

          The refractive index of the core is  $n_{core} = 1.497$

         The refractive index of the cladding  is   $n_{cladding} = 1.421$

Generally according to Snell's law

      $n_{core} * sin(90- \theta) = n_{cladding} * sin (90)$

Where $\theta_{max}$ is the largest angle a largest angle a ray will make with respect to the interface of the fiber and experience total internal reflection

      $\theta_{max} = 90 - sin^{-1} [\frac{n_{cladding}}{n_{core}} ]$

       $\theta_{max} = 90 - sin^{-1} [\frac{1.421}{1.497}} ]$

      $\theta_{max} =18.38^o$

Given from the question the the largest angle is  5°

Generally the refraction index of the cladding is mathematically represented as

           $n_{cladding} = n_{core} * sin (90 - 5)$

          $n_{cladding} =1.491$