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State the conditions of total internal r...

State the conditions of total internal reflection. Refractive indices of the given prism material for Red, Blue and Green colors are respectively 1.39, 1.48 and 1.42 respectively. Trace the path of rays through the prism.

Text Solution

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Two conditions for TIR -
(a) Light must travel from densar to rarer medium
(b) `i gt i_(c)`
`because "Sin "i_(c) = (1)/(mu)`
`therefore (i_(c))_("Red") = "Sin"^(-1)((1)/(1.39)) = 46^(@)`
`(i_(c))_("Green") = "Sin"^(-1)((1)/(1.42)) = 44.8^(@)`
`(i_(c))_("Blue") = "Sin"^(-1)((1)/(1.48)) = 43^(@)`
`because` Angle of incidence at face AC is `45^(@)` which is more than the critical angle for Blue and Green colours therefore they will show TIR but Red colour will refract to other medium.
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