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Question

A light source is located at P subscript 1 end subscript as shown in the figure. All sides of the polygon are equal. The intensity of illumination at P subscript 2 end subscript is I subscript 0 end subscript. What will be the intensity of illumination at P subscript 3 end subscript

  1. fraction numerator 3 square root of 3 over denominator 8 end fraction I subscript 0 end subscript    
  2. fraction numerator I subscript 0 end subscript over denominator 8 end fraction    
  3. fraction numerator 3 over denominator 8 end fraction I subscript 0 end subscript    
  4. fraction numerator square root of 3 over denominator 8 end fraction I subscript 0 end subscript    

The correct answer is: fraction numerator 3 square root of 3 over denominator 8 end fraction I subscript 0 end subscript


    From the geometry of the figure

    p subscript 1 end subscript p subscript 2 end subscript equals 2 a sin invisible function application 6 0 to the power of o end exponent
    so, I subscript P subscript 2 end subscript end subscript equals fraction numerator L over denominator p subscript 1 end subscript p subscript 2 end subscript superscript 2 end superscript end fraction
    equals fraction numerator L over denominator left parenthesis 2 a sin invisible function application 6 0 to the power of o end exponent right parenthesis to the power of 2 end exponent end fraction equals fraction numerator L over denominator 3 a to the power of 2 end exponent end fraction
    and I subscript P subscript 3 end subscript end subscript equals fraction numerator L over denominator left parenthesis P subscript 1 end subscript P subscript 2 end subscript superscript 2 end superscript plus a to the power of 2 end exponent right parenthesis end fraction cos invisible function application 3 0 to the power of o end exponent
    =fraction numerator L over denominator left square bracket left parenthesis 2 a sin invisible function application 6 0 to the power of o end exponent right parenthesis to the power of 2 end exponent plus a to the power of 2 end exponent right square bracket end fraction fraction numerator square root of 3 over denominator 2 end fraction equals fraction numerator square root of 3 L over denominator 8 a to the power of 2 end exponent end fraction
    rightwards double arrow I subscript P subscript 3 end subscript end subscript equals fraction numerator 3 square root of 3 over denominator 8 end fraction I subscript P subscript 2 end subscript end subscript equals fraction numerator 3 square root of 3 over denominator 8 end fraction I subscript 0 end subscript
    All options are wrong

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