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Question
Define the critical angle for a given pair of media and total internal reflection. Obtain the relation between the critical angle and refractive index of the medium.
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Solution
The angle of incidence corresponding to an angle of refraction of 90° is called the critical angle for the given pair of media. If the angle of incidence of light, when travelling from a denser medium to a rarer medium, is greater than the critical angle then total internal reflection takes place.
Let the angle of incidence i and C be the critical angle C.
Let the angle of refraction r = 90°.
The refractive index of the rarer medium is μa.
The refractive index of the denser medium is μb.
Applying Snell's law,
`(sini)/(sinr) = mu_a/mu_b`
μb sinC = μa sin90° ....[∵ i = C and r = 90°]
`mu_a/mu_b = 1/(sinC)`
Thus, we arrive at a formula expressing the critical angle and refractive index relation:
`""_amu_b = 1/(sinC)`
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