Answer
$1.70$
Work Step by Step
The required index of refraction can be determined as follows:
$\frac{sin\theta_r}{cos\theta_r}=\frac{sin 45^{\circ}}{\frac{sin 34^{\circ}}{sin 45^{\circ}}+cos 45^{\circ}}$
$\implies \theta_r=tan^{-1}(\frac{45^{\circ}}{\frac{sin 34^{\circ}}{sin 45^{\circ}}+cos 45^{\circ}})$
$\implies \theta_r=25.3^{\circ}$
Now the index can be calculated as
$n=\frac{n_{air}sin 45^{\circ}}{sin 25.3^{\circ}}$
$\implies n=1.70$
