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In the figure ABC is the cross section of a right angled prism and ACDE is the cross section of a glass slab. The value of theta so that light incident normally on the face AB does not cross the face AC is (given s i n to the power of negative 1 end exponent invisible function application left parenthesis 3 divided by 5 right parenthesis equals 37 to the power of ring operator end exponent)

  1. theta less or equal than 37 to the power of ring operator end exponent    
  2. theta less than 37 to the power of ring operator end exponent    
  3. theta less or equal than 53 to the power of ring operator end exponent    
  4. theta less than 53 to the power of ring operator end exponent    

The correct answer is: theta less than 37 to the power of ring operator end exponent



    table row cell A equals 90 to the power of ring operator end exponent minus theta end cell row cell r subscript 2 end subscript equals A equals 90 to the power of ring operator end exponent minus theta greater than theta subscript C end subscript end cell row cell c o s invisible function application theta greater than s i n invisible function application theta subscript C end subscript equals fraction numerator fraction numerator 6 over denominator 5 end fraction over denominator fraction numerator 3 over denominator 2 end fraction end fraction equals fraction numerator 4 over denominator 5 end fraction end cell row cell open parentheses theta subscript c end subscript close text end text text i end text text s end text text end text text c end text text r end text text i end text text t end text text i end text text c end text text a end text text l end text text end text text a end text text n end text text g end text text l end text text e end text text end text text ) end text text end text end cell row cell rightwards double arrow theta less than cos to the power of negative 1 end exponent invisible function application fraction numerator 4 over denominator 5 end fraction equals 37 to the power of ring operator end exponent end cell end table

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