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

A ray of light is incident on one face of an equilateral glass prism having refractive index $$\sqrt{2}$$. It produces the emergent ray which just. grazes along the adjacent face. The value of angle of incidence is $$\left(\sin 45^{\circ}=\cos 45^{\circ}=\frac{1}{\sqrt{2}}\right)$$