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Question

Three lenses L subscript 1 end subscript comma L subscript 2 end subscript comma L subscript 3 end subscript are placed co-axially as shown in figure. Focal length's of lenses are given 30 cm, 10 cm and 5 cm respectively. If a parallel beam of light falling on lens L subscript 1 end subscript, emerging L subscript 3 end subscript as a convergent beam such that it converges at the focus of L subscript 3 end subscript. Distance between L subscript 1 end subscript and L subscript 2 end subscript will be

  1. 40 cm    
  2. 30 cm    
  3. 20 cm    
  4. 10 cm    

The correct answer is: 20 cm


    According to the problem, combination of L subscript 1 end subscript and L subscript 2 end subscript act a simple glass plate. Hence according to formula fraction numerator 1 over denominator F end fraction equals fraction numerator 1 over denominator f subscript 1 end subscript end fraction plus fraction numerator 1 over denominator f subscript 2 end subscript end fraction minus fraction numerator d over denominator f subscript 1 end subscript f subscript 2 end subscript end fraction
    fraction numerator 1 over denominator f subscript 1 end subscript end fraction plus fraction numerator 1 over denominator f subscript 2 end subscript end fraction minus fraction numerator d over denominator f subscript 1 end subscript f subscript 2 end subscript end fraction equals 0 rightwards double arrow fraction numerator 1 over denominator f subscript 1 end subscript end fraction plus fraction numerator 1 over denominator f subscript 2 end subscript end fraction equals fraction numerator d over denominator f subscript 1 end subscript f subscript 2 end subscript end fraction
    rightwards double arrow fraction numerator 1 over denominator 30 end fraction minus fraction numerator 1 over denominator 10 end fraction equals fraction numerator d over denominator 30 cross times negative 10 end fraction rightwards double arrow fraction numerator negative 20 over denominator 30 cross times 10 end fraction equals negative fraction numerator d over denominator 30 cross times 10 end fraction
    rightwards double arrow d equals 20 blank c m

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