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A ray of light from a denser medium stri...

A ray of light from a denser medium strikes a rarer medium at an angle of incidence `i = tan^( -1)(1//2)`. If the reflected and the refracted rays are mutually perpendicular to each-other, what is the value of the critical angle in degree?

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From Snell’s law, we have
`(sin i)/(sinr)=mu_(R)/mu_(D)` or , `mu=mu_(D)/mu_(R)=(sinr)/(sini)`…..(i)
According to the given problem.
`i+r+90^@ =180^@` or, `r=90^@-i`
Substituting the above value of r in equation (i), we get
`mu=(sin(90^@-i))/(sini)` or, `mu=coti`....(ii)
By definition `C = sin^(-1)(1/mu)`or, `C=sin^(-1)(1/(coti))`(using equation (ii)
or`C=sin^(-1)(tani)=sin^(-1)(1//2) implies C=pi//6=30^@`
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