Physics-
General
Easy

Question

A rod of glass (mu = 1.5) and of square cross section is bent into the shape shown in the figure. A parallel beam of light falls on the plane flat surface A as shown in the figure. If d is the width of a side and R is the radius of circular arc then for what maximum value of fraction numerator d over denominator R end fraction light entering the glass slab through surface A emerges from the glass through B

  1. 1.5    
  2. 0.5    
  3. 1.3    
  4. None of these    

The correct answer is: 0.5


    Consider the figure if smallest
    angle of incidence q is greater than critical angle then all light will emerge out of B

    Þ theta greater or equal than sin to the power of negative 1 end exponent invisible function application open parentheses fraction numerator 1 over denominator mu end fraction close parentheses rightwards double arrow sin invisible function application theta greater or equal than fraction numerator 1 over denominator mu end fraction
    from figure sin invisible function application theta equals fraction numerator R over denominator R plus d end fraction
    Þ fraction numerator R over denominator R plus d end fraction greater or equal than fraction numerator 1 over denominator mu end fraction rightwards double arrow open parentheses 1 plus fraction numerator d over denominator R end fraction close parentheses less or equal than mu
    Þ fraction numerator d over denominator R end fraction less or equal than mu minus 1 rightwards double arrow open parentheses fraction numerator d over denominator R end fraction close parentheses subscript m a x end subscript

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