A ray of light passes through an equilateral prism such that the angle of incidence $$(i)$$ is equal to angle of emergence $$(e)$$. The angle of emergence is equal to $$\left(\frac{3}{4}\right)$$th the angle of prism. The angle of deviation is

The radii of curvature of both the surfaces of a convex lens of focal length $$f$$ and power $$P$$ are equal. One of the surfaces is made by plane grinding. The new focal length and focal power of the lens is

A spherical surface of radius of curvature '$$R$$' separates air from glass of refractive index 1.5. The centre of curvature is in the glass. A point object $$\mathrm{P}$$ placed in air forms a real image $$\mathrm{Q}$$ in the glass. The line $$P Q$$ cuts the surface at point '$$O$$' and $$\mathrm{PO}=\mathrm{OQ}=\mathrm{x}$$. Hence the distance '$$\mathrm{x}$$' is equal to

Array of light is incident at an angle of incidence '$$i$$' on one surface of a prism of small angle $$\mathrm{A}$$ and emerges normally from the other surface. If the refractive index of the material of the prism is '$$\mu$$', then the angle of incidence is equal to