Four rays $1, 2, 3$ and $4$ are incident normally on the face $PQ$ of an isosceles prism $PQR$ with apex angle $\angle Q = 120^{\circ}$. The refractive indices of the material of the prism for the above rays $1, 2, 3$ and $4$ are $1.85, 1.95, 2.05$ and $2.15$ respectively and the surrounding medium is air. Then,the rays emerging from the face $QR$ are

$A$ glass prism whose cross-section is an isosceles triangle stands with its (horizontal) base in water; the angles that its two equal sides make with the base are each $\theta$. An incident ray of light,above and parallel to the water surface,is totally internally reflected at the glass-water interface and subsequently re-emerges into the air. Take the refractive indices of glass and water to be $\frac{3}{2}$ and $\frac{4}{3}$,respectively. The maximum value of $\cos\theta$ is:

$A$ small source of light is $4 \ m$ below the surface of a liquid of refractive index $5/3$. In order to cut off all the light coming out of the liquid surface,the minimum diameter of the disc placed on the surface of the liquid is .......... $m$.

$A$ ray of light enters from air into a denser medium of refractive index $\mu = \frac{4}{3}$,as shown in the figure. The light ray undergoes total internal reflection at the adjacent surface as shown. The maximum value of angle $\theta$ should be equal to -

$A$ water-proof laser pointer of length $10 \,cm$ is placed in a water tank. It rotates about a horizontal axis passing through its centre of mass in a vertical plane as shown in the figure. The time period of rotation is $60 \,s$. Assuming the water to be still and no reflections from the surface of the tank, the duration for which the light beam escapes the tank in one time period is close to ............. $s$. (Take, refractive index of water $= 1.33$)

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