Physics-
General
Easy

Question

Two thin convex lenses of focal lengths f1 and f2 are separated by a horizontal distance d text  (where  end text d less than f subscript 1 end subscript comma d less than f subscript 2 end subscript text  ) end text and their centers are displaced by a vertical separation D as shown in the figure : Taking the origin of coordinates, O, at the center of the first lens, the x and y-coordinates of the focal point of this lens system, for a parallel beam of rays coming from the left, are given by :

  1. x equals fraction numerator f subscript 1 end subscript f subscript 2 end subscript over denominator f subscript 1 end subscript plus f subscript 2 end subscript end fraction comma y equals D    
  2. x equals fraction numerator f subscript 1 end subscript open parentheses f subscript 2 end subscript plus d close parentheses over denominator f subscript 1 end subscript plus f subscript 2 end subscript minus d end fraction comma y equals fraction numerator capital delta over denominator f subscript 1 end subscript plus f subscript 2 end subscript end fraction    
  3. x equals fraction numerator f subscript 1 end subscript f subscript 2 end subscript plus d open parentheses f subscript 1 end subscript minus d close parentheses over denominator f subscript 1 end subscript plus f subscript 2 end subscript minus d end fraction comma y equals fraction numerator capital delta open parentheses f subscript 1 end subscript minus d close parentheses over denominator f subscript 1 end subscript plus f subscript 2 end subscript minus d end fraction    
  4. x equals fraction numerator f subscript 1 end subscript f subscript 2 end subscript plus d open parentheses f subscript 1 end subscript minus d close parentheses over denominator f subscript 1 end subscript plus f subscript 2 end subscript minus d end fraction comma y equals 0    

The correct answer is: x equals fraction numerator f subscript 1 end subscript f subscript 2 end subscript plus d open parentheses f subscript 1 end subscript minus d close parentheses over denominator f subscript 1 end subscript plus f subscript 2 end subscript minus d end fraction comma y equals fraction numerator capital delta open parentheses f subscript 1 end subscript minus d close parentheses over denominator f subscript 1 end subscript plus f subscript 2 end subscript minus d end fraction

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