The critical angle is expressed as:

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

Snell's law:

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

This can be expressed in the diagram below;

θ_{c} = sin^{-1}(1/1.34) = 48.2°

A ray of light is incident in air on a block of a transparent solid whose index of refraction is n. If n = 1.34, what is the largest angle of incidence for which total internal reflection will occur at the vertical face (point shown in the figure )?

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