Q1 A ray is travelling in a medium with refractive index n; and is incident on a flat interface with a medium with a refractive index of nt. (a) Determine the matrix which describes how the incident ray vector, (1), is refracted at this interface. [10] An alternative formulation of the ray vector replaces its angle component with the "optical direction cosine", no where n is the refractive index of the medium in which the ray is travelling. Hence the ray vector becomes (n). (b) Using the optical direction cosine form of the ray vector, determine the matrix for refraction at the same flat interface from part (a). [10] (c) Using the optical direction cosine form of the ray vector, determine the translation matrix for a ray translated a distance d parallel to the optical axis in a medium with a refractive index of n. [10] (d) Based on your answers to (b) and (c), explain quantitatively how an object submerged in water appears to an observer looking from above, assuming a flat water surface. [10]