A ray of light travelling in a rarer medium strikes a plane boundary between the rarer medium and a denser medium at an angle of incidence 'i' such that the reflected and the refracted rays are mutually perpendicular. Another ray of light of same frequency is incident on the same boundary from the side of denser medium. Find the minimum angle of incidence at the denser-rarer boundary so that the second ray is totally reflected

Explanation

Figure shows incidence of a ray at the rarer-denser boundary such that reflected and refracted rays are mutually perpendicular.
` i.e.r+90^@ +r’=180^@`. or
`r = 90^@ - r = 90^@ - i`[r=i, law of reflection]
Apply Snell.s law at the boundary,
` therefore mu_R sin i= mu _D sin r .`
` mu_R sin i = mu _D sin (90^@ -i) = mu_D cos i`
` or ( mu_D)/(mu_R) = tan i`
`sin theta_C =(1)/( ""_(R )mu_D )= (1)/(mu_D //mu_R) = (mu_R)/( mu_D) `
Using equation (1),
` sin theta_c =(1)/( tan i ) = cot i`
` = theta_c =sin^(-1) ( cot i)`