For a given pair of transparent media,the critical angle is maximum for which colour?

With respect to air,the critical angle in a medium for red light of wavelength $\lambda_1$ is $\theta$. Other facts remaining same,the critical angle for yellow light of wavelength $\lambda_2$ will be

What is the least radius through which an optical fiber of core diameter $0.05 \, mm$ may be bent (as shown in figure) without serious loss of light (in $, mm$)? The refractive index of the core is $1.6$ and that of cladding is $1.5$.

$A$ ray of light travels from a medium of refractive index $2$ to another medium of refractive index $\sqrt{2}$. Total internal reflection takes place when the angle of incidence is

Why is mirage formation seen in deserts during the summer?

Material $A$ has a critical angle ${i_A},$ and material $B$ has a critical angle ${i_B}$ $({i_B} > {i_A})$. Then which of the following is true?
$(i)$ Light can be totally internally reflected when it passes from $B$ to $A$.
$(ii)$ Light can be totally internally reflected when it passes from $A$ to $B$.
$(iii)$ The critical angle for total internal reflection is ${i_B} - {i_A}$.
$(iv)$ The critical angle between $A$ and $B$ is ${\sin ^{ - 1}}\left( {\frac{{\sin {i_A}}}{{\sin {i_B}}}} \right)$.