(i) Relation between critical angle $\theta_c$ and refractive index $\mu$:

$$\sin\theta_c = \frac{1}{\mu} \Rightarrow \theta_c = \sin^{-1}\left(\frac{1}{\mu}\right)$$

Higher $\mu$ $\Rightarrow$ smaller $\theta_c$.

(ii) Yes, critical angle depends on the colour of light.

Since $\mu$ varies with wavelength (colour), $\theta_c$ also varies:

• Violet (shortest $\lambda$, highest $\mu$) has minimum $\theta_c$.
• Red (longest $\lambda$, lowest $\mu$) has maximum $\theta_c$.