The index of refraction of the core of a typical fiber optic is n_{core} core  = 1.51; the cladding has n_{clad} clad  = 1.43. calculate the critical angles for the total internal reflection i_{crit}i crit  and α_{crit}α crit .

Refrigerant-134a flows through a carnot heat pump cycle at 0.5 kg/s. it is known that the maximum absolute temperature in the cycle is 1.1 times the minimum absolute temperature, and the net power input to the cycle is 2.5 kw. if the refrigerant changes from a saturated vapor to a saturated liquid during the heat rejection process, determine the maximum magnitude of the enthalpy of vaporization for this process in kj/kg (with 3 significant figures).