$5.[20$ points$]$ Fiber optic cables are used in the oil and gas industry to transmit data from sensers thousands of feet deep to the surface due to their ability to transmit light long distances with minimal signal loss. A fiber optic cable consists of a glass core and cladding $($lower refractive index to keep light confined$).$ If silica glass has a refractive index of $1\mathrm{.}40$ and the cladding has a refractive index of $1\mathrm{.}37,$ what is: