Total internal reflection, Physics

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Light is shined into a glass rod. To guarantee the total internal reflection (TIR) happens to all the possible rays, what is the minimum index of refraction n for the glass?

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Hint: To make sure all rays TIR inside the rod, you just need to consider an extreme case, i.e., the incident angle q₁ (on the top surface of glass rod) equals to 90^o.

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