b
\(\,{n_{eff}}\, = \,\,{n_0}\,\sqrt {1\,\, - \,\,\left( {\frac{{80.5\,N}}{{{\nu ^2}}}} \right)} \,\, = \,\,1\,\sqrt {1\,\, - \,\,\frac{{80.5\,\, \times \,\,(400\,\, \times \,\,{{10}^6})}}{{{{(55\,\, \times \,\,{{10}^6})}^2}}}} \,\, \approx \,\,1\)

\({n_{eff}}\, = \,\,\frac{{\sin \,i}}{{\sin \,r}}\,\,\, \Rightarrow \,\,\sin \,r\,\, = \,\,\sin \,i\,\, \Rightarrow \,\,r\, = \,\,i\,\, = \,\,{45^ \circ }\)