Physics - Geometrical Optics Question with Solution | TestHub

The critical angle $C$ for a medium is given by the relation $\sin C=\frac{1}{\mu }$, where $\mu$ is the refractive index of the medium.

According to Cauchy's equation, the refractive index $\mu$ depends on the wavelength $\lambda$ of light as $\mu =A+\frac{B}{{\lambda }^2}$. Thus, $\mu$ decreases as $\lambda$ increases.

The order of wavelengths for the visible spectrum is:
${\lambda }_V<{\lambda }_I<{\lambda }_B<{\lambda }_G<{\lambda }_Y<{\lambda }_O<{\lambda }_R$

Consequently, the refractive indices follow the reverse order:
${\mu }_V>{\mu }_I>{\mu }_B>{\mu }_G>{\mu }_Y>{\mu }_O>{\mu }_R$

Since $\sin C=\frac{1}{\mu }$, the critical angles for the respective colors will be in the order:
$C_V<C_I<C_B<C_G<C_Y<C_O<C_R$

The problem states that green light is just totally internally reflected, which means the angle of incidence $i$ is exactly equal to the critical angle for green light ($i=C_G$).

For total internal reflection to occur for a specific color, the angle of incidence $i$ must be greater than its critical angle ($i>C$).

Since $i=C_G$, we have:
$i>C_V$
$i>C_I$
$i>C_B$

Therefore, violet, indigo, and blue light will undergo total internal reflection and will be present in the reflected rays inside the glass. The colors yellow, orange, and red have critical angles greater than $i$, so they will be refracted into the air.

Answer: violet, indigo, blue