Answer
The required value of $n_{1}$ is $1.4$.
Work Step by Step
From (a), we have that $n_{1}\sin\theta_{1} = n_{2}\sin\theta_{2}$
\[\implies n_{1} = \frac{n_{2}\sin\theta_{2}}{\sin\theta_{1}}\]
Given that $\theta_{1} = 55^\circ, \theta_{2} = 35^\circ$ and $n_{2} = 2$.
\[\implies n_{1} = \frac{2\sin35^\circ}{\sin55^\circ}\]
\[\implies n_{1} = 1.4\]
