A ray of light while travelling from a denser to a rarer medium undergoes total internal reflection. Derive the expression for the critical angle in terms of the speed of light in the respective media.

A ray of light while travelling from a denser to a rarer medium underg

1.	A ray of light while travelling from a denser to a rarer medium undergoes total internal reflection. Derive the expression for the critical angle in terms of the speed of light in the respective media.
Answer» Solution : As shown in Fig. 9.36, if IC be the CRITICAL angle in a given denser medium number 2 with respect to a rarer medium number 1, then `sin i_( c) = n_(12) = p_(2)/p_(1) = ("speed of light in denser medium")/("speed of light in rarer medium")` If rarer medium be free space or air, then the RELATION is modified as: `sin i_( c) = ("speed of light in denser medium")/("speed of light in free space") = v/c`

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A ray of light while travelling from a denser to a rarer medium undergoes total internal reflection. Derive the expression for the critical angle in terms of the speed of light in the respective media.

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