Two Lenses in Contact. (a) Prove that when two thin lenses with focal lengths f1 and...

Two Lenses in Contact. (a) Prove that when two thin lenses with focal lengths f₁ and f₂ are placed in contact, the focal length ƒ of the combination is given by the relationship

(b) A converging meniscus lens (see Fig. 34.32a) has an index of refraction of 1.55 and radii of curvature for its surfaces of magnitudes 4.50 cm and 9.00 cm. The concave surface is placed upward and filled with carbon tetrachloride (CCl₄), which has n = 1.46. What is the focal length of the CCl₄-glass combination?