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
The speed of light in two media $$M_1$$ and $$M_2$$ are $$1.5 \times 10^8$$ $$\mathrm{m} / \mathrm{s}$$ and $$2 \times 10^8 \mathrm{~m} / \mathrm{s}$$ respectively. If the light undergoes total internal reflection, the critical angle between the two media is
The minimum distance between an object and its real image formed by a convex lens of focal length 'f' is
An object is located on a wall, its image of equal size is to be obtained on a parallel wall with the help of a convex lens. The lens is placed at a distance '$$\mathrm{d}$$' in front of the second wall. The required focal length of the lens is