An achromatic doublet is constructed by combining two thin lenses in contact of focal lengths and made of glasses with dispersive powers and . What is the condition for achromatism?

Answer and explanation

Correct answer: B.

  1. Step 1: For a combination of lenses in contact, the net focal length is .
  2. Step 2: Differentiating with respect to refractive index to eliminate chromatic aberration yields .
  3. Step 3: Since dispersive power is , this simplifies directly to the condition .
Answer
.
Why not the others: multiplies instead of dividing; has incorrect powers; is impossible with non-zero net power.

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