b
Snell's law \(\mu_1 \sin 45^{\circ}=\mu_2 \sin 30^{\circ}\)

\(\frac{\mu_1}{\mu_2}=\frac{1}{\sqrt{2}}\)

\(\Rightarrow \frac{\mu_1}{\mu_2}=\frac{\lambda_2}{\lambda_1}=\frac{1}{\sqrt{2}}\)

\(\Rightarrow \lambda_2=\frac{\lambda_1}{\sqrt{2}}\)

Frequency doesn't change on change in medium.