Can you please provide a response to each part of the practice problem? Please include all steps/identities used for each part for my understanding, thanks! (this has to do with the physical science of light rays AKA photonics) Please no reposts.

Practice Problem 3. Consider the optical doublet shown below. It consists of a positive lens (lens 1) of crown glass (refractive index n; = 1.52) and a negative lens (lens 2) of flint glass (refractive index n3 = 1.62). The thickness of lens 1 is t; = 1 cm and the thickness of lens 2 is t; = 0.5 cm. The radius of curvature is 20 cm for all refracting surfaces. Assume the paraxial approximation holds. Input plane output plane Air Air Lens 1 Lens 2 The input and output planes are on the surfaces of the lens as shown in the figure. i. Find the ray transfer matrix of the system. ii. What is the focal length of the system? iii. Does the doublet act like a positive or a negative focal length lens? (Such lens combinations are sometimes used in optical instruments to reduce chromatic dispersion and are called achromatic doublet.)