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It is desired to make a converging achromatic combination of mean focal length 50 cm by using two lenses of materials A and B . If the dispersive power of A and B are in ratio 1 : 2 , the focal lengths of the convex and the concave lenses are respectively

Options

  1. A25 cm and 50 cm
  2. B50 cm and 25 cm
  3. C50 cm and 100 cm
  4. D100 cm and 50 cm

Correct answer

A. 25 cm and 50 cm

Step-by-step solution

ω 1 ω 2 = 1 2 Now, f 1 f 2 = - ω 1 ω 2 = - 1 2 Or f 2 = - 2 f 1 Now, 1 F = 1 f 1 + 1 f 2 1 50 = 1 f 1 + 1 - 2 f 1 Or 50 f = - 2 + 1 - 2 f 1 = 1 2 f 1 Or 2 f 1 = 50 or f 1 = 25 c m Again f 2 = − 2 × 25 cm f 2 = − 50 cm

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