A double convex air bubble in water behaves as

If a ray of light in denser medium strikes a rarer medium at angle of incidence $$i$$, the angles of reflection and refraction are $$r$$ and $$r^{\prime}$$ respectively. If the reflected and refracted rays are at right angles to each other, the critical angle for the given pair of media is

A transparent glass cube of length $$24 \mathrm{~cm}$$ has a small air bubble trapped inside. When seen normally through one surface from air outside, its apparent distance is $$10 \mathrm{~cm}$$ from the surface. When seen normally from opposite surface, its apparent distance is $$6 \mathrm{~cm}$$. The distance of the air bubble from first surface is

The angle of prism is $$A$$ and one of its refracting surface is silvered. Light rays falling at an angle of incidence '$$2 \mathrm{A}$$' on the first surface return back through the same path after suffering reflection at the silvered surface. The refractive index of the material of the prism is