A ray ${\mathrm{R}}_1$ is incident on the plane surface of the glass slab (kept in the air) of refractive index $\sqrt{2}$ at an angle of incidence equal to the critical angle for this air-glass system. The refracted ray ${\mathrm{R}}_2$ undergoes partial reflection and refraction at the other surface. The angle between the reflected ray ${\mathrm{R}}_3$ and the refracted ray ${\mathrm{R}}_4$ at that surface is:

 

Bottom face of the glass cube is silvered as shown. A ray of light is incident on the top face of the cube a shown. Find the deviation of the ray when it comes out of the glass cube.

The distance of final image from $\mathrm{AB}$ as observed by observer $\mathrm{P}$ is:

A ray of light is incident upon an air/water interface ( it passes from air into water) at  an angle of $45°$. Which of the following quantities change as the light enter the water?

(I) wavelength

(II) frequency

(III) speed of propagation 

(IV) direction of propagation

A paraxial beam is incident on a glass $\left(\mathrm{n}=1.5\right)$ hemisphere of radius $\mathrm{R}=6\mathrm{cm}$ in air as shown. The distance of point of convergence $\mathrm{F}$ form the plane surface of hemisphere  is: