You are given a plano-convex lens. The glass has a refractive index of 1.5. The magnitude of radius of curvature of the convex surface is 100 mm. You want to make the image 2 m from an object using the lens. You want the image to be as small as possible.

a. What is the focal length of the lens?

b. How far from the object should you place the lens?

c. If the object is 7 cm tall, how tall will the image be?

Please include a diagram for reference, explanation in words, and calculations to show all work. Thank you.