(1)

The critical angle in the case of total internal reflection is directly proportional to wavelength of light.

$i_c\propto \lambda$

Yellow, orange, red emerge from air.

$\lambda$ is inversely proportional to refractive index of the medium.

Hence, critical angle will be greater for constituents of light having larger wavelength (than green).

(2)

For air, $c=\frac{x}{t_1}$

For medium, $v=\frac{10x}{t_2} ; \mu =\frac{c}{v}=\frac{x\times t_2}{t_1\times 10x}=\frac{t_2}{10t_1}$

$\sin C=\frac{1}{\mu }=\frac{10t_1}{t_2} ; C={\sin }^{-1}\left[\frac{{\displaystyle 10t_1}}{{\displaystyle t_2}}\right]$

(2)

For medium A, speed of light $v_A=1.5\times {10}^8\text{m/s}$

For medium B, speed of light $v_B=2.0\times {10}^8\text{m/s}$

For medium A, $n_A=\frac{c}{v_A}=\frac{3\times {10}^8}{1.5\times {10}^8}=2$

For medium B, $n_B=\frac{c}{v_B}=\frac{3\times {10}^8}{2\times {10}^8}=1.5$

The critical angle for a ray of light is,

$\sin C=\frac{n_B}{n_A} ; C={\sin }^{-1}\left(\frac{{\displaystyle 1.5}}{{\displaystyle 2}}\right) ; C={\sin }^{-1}(0.750)$

(1)

When the angle of refraction is equal to 90°, the angle of incidence is called the critical angle.