A double-convex lens is to be made of a transparent material with an index of refraction of 1.4. One surface is to have twice the radius of curvature of the other and the focal length is to be 54 mm. What is the magnitude of the (a) smaller and (b) larger radius? (a) Number i Units (b) Number i Units

You are designing a lens to be made of glass with index of refraction 1.70. The first surface (the surface toward the object) is to be convex with radius of curvature 28.0 cm, and the focal length of the lens is to be 14.0 cm. (a) What must be the radius of curvature of the second surface (the surface away from the object)? (b) Will the second surface be concave or convex?

A thick-walled wine goblet can be considered to be a hollow glass sphere with an outer radius of 4.10 cmcm  and an inner radius of 3.60 cmcm. The index of refraction of the goblet glass is 1.50. (a) A beam of parallel light rays enters the side of the empty goblet along a horizontal radius. Where, if anywhere, will an image be formed? (b) The goblet is filled with white wine (nn = 1.37). Where is the image formed? Use the image from the previous part as the object for the second surface (the inner wall of the same side of the goblet) and find the position of the second image. Express your answer with the appropriate units.

A glass lens (?=1.60) has a focal length of ?=−32.7 cm and a plano‑concave shape. Calculate the magnitude R of the radius of curvature of the concave surface. R = ?cm If a lens is constructed from the same glass to form a plano‑convex shape with the same radius of curvature magnitude, what will the focal length f' be? f' = ? cm