6 Light rays enter the plane surface of a glass hemisphere of radius 5 cm and refractive index 1.5. a. Using the system matrix representing the hemisphere, de- termine the exit elevation and angle of a ray that enters parallel to the optical axis and at an elevation of 1 cm. b. Enlarge the system to a distance x beyond the hemi- sphere and find the new system matrix as a function of x. c. Using the new system matrix, determine where the ray described above crosses the optical axis.

6 Light rays enter the plane surface of a glass hemisphere of radius 5 cm and refractive index 1.5. a. Using the system matrix representing the hemisphere, de- termine the exit elevation and angle of a ray that enters parallel to the optical axis and at an elevation of 1 cm. b. Enlarge the system to a distance x beyond the hemi- sphere and find the new system matrix as a function of x. c. Using the new system matrix, determine where the ray described above crosses the optical axis.