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

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

1/f = 1 / f1 + 1/f2

(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 magni- tudes 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?