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

A glass prism deviates the red and violet rays through $$9^{\circ}$$ and $$11^{\circ}$$ respectively. A second prism of equal angle deviates them through $$11^{\circ}$$ and $$13^{\circ}$$ respectively. The ratio of dispersive power of second prism to first prism is