Snell's law:

$\overline{){{\mathbf{\eta}}}_{{\mathbf{1}}}{\mathbf{s}}{\mathbf{i}}{\mathbf{n}}{{\mathbf{\theta}}}_{{\mathbf{1}}}{\mathbf{=}}{{\mathbf{\eta}}}_{{\mathbf{2}}}{\mathbf{s}}{\mathbf{i}}{\mathbf{n}}{{\mathbf{\theta}}}_{{\mathbf{2}}}}$

Critical angle:

$\overline{){{\mathbf{\theta}}}_{{\mathbf{c}}}{\mathbf{=}}{\mathbf{s}}{\mathbf{i}}{{\mathbf{n}}}^{\mathbf{-}\mathbf{1}}{\mathbf{\left(}}\frac{{\mathbf{\eta}}_{\mathbf{2}}}{{\mathbf{\eta}}_{\mathbf{1}}}{\mathbf{\right)}}}$

**a)**

θ_{max} = 90° - θc

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 (*n _{core}* = 1.483 ) and the cladding (

a) Numerically, what is the largest angle (in degrees) a ray will make with respect to the interface of the fiber *θ _{max}*, and still experience total internal reflection?

b) Suppose you wanted the largest angle at which total internal reflection occurred to be *θ*_{max} = 5 degrees. What index of refraction does the cladding need if the core is unchanged?

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