The colour for which the critical angle is maximum in water-air system is

For water – air system let C is critical angle

${\mu }_{\text{w}}\sin \text{c}={\mu }_{\text{air}}$

$\sin c=\frac{1}{{\mu }_{\text{water}}}$

But refractive index of a medium  $\mu$depends on the wavelength of light  $\lambda$. The relation between  $\mu ,\lambda$in a particular medium can be given as

$\mu =\text{A}+\frac{\text{B}}{{\lambda }^2}$

In a particular medium if  $\lambda$ increases then $\mu$decreases.

We have red colour with maximum wavelength & violet with minimum wavelength

${\lambda }_{\text{R}}>{\lambda }_{\text{v}}$So

$\Rightarrow {\mu }_{\text{R}}<{\mu }_{\text{v}}$

Critical angle for red ${\text{C}}_{\text{R}}$, critical angle for violet is ${\text{C}}_{\text{V}}$

$\frac{1}{\sin {\text{C}}_{\text{R}}}<\frac{1}{\sin {\text{C}}_{\text{V}}}$

${\text{C}}_{\text{R}}>{\text{C}}_{\text{V}}$

In VIAGYOR (seven colours)

${\text{c}}_{\text{V}}<{\text{c}}_I<{\text{c}}_{\text{B}}<{\text{c}}_{\text{G}}<{\text{c}}_{\text{Y}}<{\text{c}}_{\text{O}}<{\text{c}}_{\text{R}}$

Hence the maximum critical angle for water – air interface is maximum for red