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

A vessel is half filled with a liquid of refractive index $$\mu$$. The other half of the vessel is filled with an immiscible liquid of refractive index $$2 \mu$$. The apparent depth of the vessel is $$50 \%$$ of the actual depth. Then $$\mu$$ is

A mosquito O is sitting infront of a glass rod having spherical end of radius of curvature 40 cm. The image would be formed at

An achromatic convergent doublet of two lenses in contact has a power of +5 D. The power of converging lens is +6 D. The ratio of the dispersive power of the convergent and divergent lenses is