The dispersive powers of the materials of the two lenses are in the ratio 4 : 3. If the achromatic combination of these two lenses in contact is a convex lens of focal length 60 cm then the focal lengths of the component lenses are
Options

Question

The dispersive powers of the materials of the two lenses are in the ratio 4 : 3. If the achromatic combination of these two lenses in contact is a convex lens of focal length 60 cm then the focal lengths of the component lenses are

Options

G1 Physics · Accepted Answer

Derived solution: Step 1: For thin prisms/lenses use dispersion relations. For an achromatic doublet, ω₁P₁ + ω₂P₂ = 0, while the net power is P₁ + P₂. Step 2: Substitute the values given in the question and apply the geometry/sign convention shown. Step 3: On simplification the result is 15 cm and - 20 cm. Therefore the correct option is D.