b
(b) From figure \(A = {r_1} + c = {r_1} + {\sin ^{ - 1}}\left({\frac{1}{\mu }} \right)\)

\( \Rightarrow {r_1} = 75 - {\sin ^{ - 1}}\left({\frac{1}{\mu }} \right)\)

\( \Rightarrow 75 - 45 = {30^o}\)

From Snell’s law At \( B\)

\(\mu = \frac{{\sin i}}{{\sin {r_1}}}\)\( \Rightarrow \sqrt 2 = \frac{{\sin i}}{{\sin {{30}^o}}}\)\( \Rightarrow i = {45^o}\)