A flint glass convex lens of focal length 16 cm is placed in contact with crown glass lens. The refractive indices of crown glass for violet and red colour are μv = 1.525, μr = 1.515 and for flint glass μv' = 1.655 and μr' = 1.645. (a) Find the nature and focal length of the crown glass lens which will form an achromatic combination with the flint glass lens. (b) What is the focal length of the combination?
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Question

A flint glass convex lens of focal length 16 cm is placed in contact with crown glass lens. The refractive indices of crown glass for violet and red colour are μv = 1.525, μr = 1.515 and for flint glass μv' = 1.655 and μr' = 1.645. (a) Find the nature and focal length of the crown glass lens which will form an achromatic combination with the flint glass lens. (b) What is the focal length of the combination?

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 f(crown) = - 20 cm; f(combination) = + 80 cm, convergent achromatic lens. Therefore the correct option is D.