[UPSC IFoS 2023] Geometrical Optics (Q125, 15M)

An achromatic doublet of focal length 25\text{ cm} is to be made by placing a convex lens of borosilicate crown glass in contact with a diverging lens of dense flint glass. Assuming n_r = 1 \cdot 61864, n_b = 1 \cdot 62468, n_r' = 1 \cdot 71426 and n_b' = 1 \cdot 72906, calculate the focal length of each lens. Here, the unprimed and the primed quantities refer to the borosilicate crown glass and dense flint glass respectively.