Physics-
General
Easy

Question

Two identical glass rode S subscript 1 end subscript and S subscript 2 end subscript (refractive index = 1.5) have one convex end of radius of curvature 10 cm. They are placed with the curved surfaces at a distance d as shown in the figure, with their axes (shown by the dashed line) aligned. When a point source of light P is placed inside rod S subscript 1 end subscript on its axis at a distance of 50 cm from the curved face, the light rays emanating from it are found to be parallel to the axis inside S subscript 2 end subscript. The distance d is

  1. 60 cm    
  2. 70 cm    
  3. 80 cm    
  4. 90 cm    

The correct answer is: 70 cm



    table row cell fraction numerator mu subscript 2 end subscript over denominator v end fraction minus fraction numerator mu subscript 1 end subscript over denominator u end fraction equals fraction numerator mu subscript 2 end subscript minus mu subscript L end subscript over denominator R end fraction end cell row cell fraction numerator 1 over denominator v end fraction minus fraction numerator 1.5 over denominator negative 50 end fraction equals fraction numerator 1 minus 1.5 over denominator negative 10 end fraction end cell row cell fraction numerator 1 over denominator v end fraction plus fraction numerator 15 over denominator 500 end fraction equals fraction numerator 5 over denominator 100 end fraction end cell row cell rightwards double arrow fraction numerator 1 over denominator v end fraction equals fraction numerator 1 over denominator 20 end fraction minus fraction numerator 3 over denominator 100 end fraction equals fraction numerator 5 minus 3 over denominator 100 end fraction end cell row cell fraction numerator 1 over denominator v end fraction equals fraction numerator 2 over denominator 100 end fraction end cell row cell v equals fraction numerator 100 over denominator 2 end fraction equals 50 end cell row cell text end text text n end text text o end text text w end text text end text text f end text text o end text text r end text text end text S text end text text. end text text end text end cell end table
    table row cell fraction numerator mu subscript 2 end subscript over denominator v end fraction minus fraction numerator mu subscript 1 end subscript over denominator u end fraction equals fraction numerator mu subscript 2 end subscript minus mu subscript 1 end subscript over denominator R end fraction end cell row cell u equals negative x v rightwards arrow infinity end cell row cell fraction numerator 1.5 over denominator infinity end fraction minus fraction numerator 1 over denominator x end fraction equals fraction numerator 1.5 minus 1 over denominator 10 end fraction end cell row cell x equals plus 20 d equals 50 plus 20 equals 70 c m end cell end table

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