In the figure shown,for an angle of incidence $i$ at the top surface,the minimum refractive index $\mu$ needed for total internal reflection at the vertical surface will be

Brilliance of diamond is due to

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

$A$ ray of light incident parallel to the base $PQ$ of an isosceles right-angled triangular prism $PQR$ suffers two successive total internal reflections at the faces $PQ$ and $QR$ before emerging reversed in direction as shown below. If the refractive index of the material of the prism is $\mu$,then

$A$ ray of light in a liquid of refractive index $1.4$ approaches the boundary surface between the liquid and air at an angle of incidence whose sine is $0.8$. Which of the following statements is correct about the behavior of the light?

With respect to air,the critical angle in a medium for light of red colour $[{\lambda _1}]$ is $\theta$. Other factors remaining the same,the critical angle for light of yellow colour $[{\lambda _2}]$ will be: