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

Question

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, 25 cm and 50 cm, 50 cm and 25 cm, 50 cm and 100 cm, 100 cm and 50 cm

MARKS App · Accepted Answer

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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