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A light beam is traveling from Region I to Region IV (Refer Figure). The refractive index in Regions I, II, III and IV are n subscript 0 end subscript comma fraction numerator n subscript 0 end subscript over denominator 2 end fraction comma fraction numerator n subscript 0 end subscript over denominator 6 end fraction text  and  end text fraction numerator n subscript 0 end subscript over denominator 8 end fraction respectively. The angle of incidence theta for which the beam just misses entering Region IV is

  1. s i n to the power of negative 1 end exponent invisible function application open parentheses fraction numerator 3 over denominator 4 end fraction close parentheses    
  2. s i n to the power of negative 1 end exponent invisible function application open parentheses fraction numerator 3 over denominator 8 end fraction close parentheses    
  3. s i n to the power of negative 1 end exponent invisible function application open parentheses fraction numerator 1 over denominator 4 end fraction close parentheses    
  4. s i n to the power of negative 1 end exponent invisible function application open parentheses fraction numerator 1 over denominator 3 end fraction close parentheses    

The correct answer is: s i n to the power of negative 1 end exponent invisible function application open parentheses fraction numerator 3 over denominator 8 end fraction close parentheses


    As the beam just suffers TIR at interface of region III and IV.

    table row cell n subscript 0 end subscript s i n invisible function application theta equals fraction numerator n subscript 0 end subscript over denominator 2 end fraction s i n invisible function application theta subscript 1 end subscript equals fraction numerator n subscript 0 end subscript over denominator 6 end fraction s i n invisible function application theta subscript 2 end subscript equals fraction numerator n subscript 0 end subscript over denominator 8 end fraction s i n invisible function application 90 to the power of ring operator end exponent end cell row cell s i n invisible function application theta equals fraction numerator 1 over denominator 8 end fraction rightwards double arrow theta equals s i n to the power of negative 1 end exponent invisible function application fraction numerator 1 over denominator 8 end fraction end cell end table

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