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Two optical media have a plane boundary between them. Suppose θ1cr is the critical angle of incidence of a beam and θ1 is the angle of incidence at which the refracted beam is perpendicular to the reflected one (the beam is assumed to come from an optically denser medium). Find the relative refractive index of these media if sin θ1cr/sin θ1 = η = 1.28.

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Let two optical mediums of R.I.n1 and n2 respectively be such that n1 > n2 . In the case when angle of incidence is θ1cr (Fig.), from the law of refraction

In the case , when the angle of incidence is θ1 , from the law of refraction at the interface of mediums 1 and 2 . 

n1 sin θ1 = n2 sin θ​​​​​​​2 

But in accordance with the problem 

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