The frequency of a light wave in a material is $2 \times 10^{14} \mathrm{~Hz}$ and wavelength is $5000 \mathop {\rm{A}}\limits^{\rm{o}} $. The refractive index of material will be

Power of biconvex lens is $ P $ diopter. When it is cut into two symmetrical halves by a plane containing the principal axis. The ratio of power of two halves is

The magnifying power of a telescope is 9 . When it is adjusted for parallel rays, the distance between the objective and eyepiece is 20 cm . The ratio of focal length of objective lens to focal length of eyepiece is found to be $ m $, then the value of $ m $ is

A thin plano-convex lens of focal length $$f$$ is split into two halves one of the halves is shifted along the optical axis. The separation between object and image formed by one of the half-lenses is 2.4 and the magnification of same lens is 2. If $$f$$ and $$d$$ be the focal length of the lens and separation between the two halves respectively then