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An achromatic convergent doublet of two lenses in contact has a power +2 D . The convex lens has power +5 D . The ratio of the dispersive powers of the convergent and divergent lenses is (in magnitude)

Options

  1. A3: 5
  2. B2: 5
  3. C4: 5
  4. D5: 6

Correct answer

A. 3: 5

Step-by-step solution

The total power of the achromatic doublet is P = P₁ + P₂ , where P₁ = +5 , D and P = +2 , D . Therefore, the power of the second lens is P₂ = 2 - 5 = -3 , D , indicating it is a divergent lens. For an achromatic combination, the dispersion condition is ₁ P₁ + ₂ P₂ = 0 . Substituting P₁ = +5 and P₂ = -3 , we have 5 ₁ - 3 ₂ = 0 , which simplifies to 5 ₁ = 3 ₂ . The ratio of the dispersive powers is ₁ ₂ = 3 5 . This corresponds to a ratio of 3:5 . Final answer: A

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