A film with thickness index nf is placed between two media with indices n1 and n2. (a) For light incident normally, passing from 1 to 2, find the value of nf that maximizes the net transmittance, T1f2, and determine this optimal value. (Hint: Instead of maximizing T1f2 itself, it is easier to maximize its natural logarithm.) (b) Compare the minimal reflective loss (1-T1f2), the value it would have in the absence of the film for the two cases: (1) n1=1.44, n2=1.69; and (2) an air-diamond interface, n1=1.00, n2=2.40.