Two similar thin equi-convex lenses, of focal length f each, are kept coaxially in contact with each other such that the focal length of the combination is F₁. When the space between the two lenses is filled with glycerin (which has the same refractive index (m = 1.5) as that of glass) then the equivalent focal length is F₂. The ratio F₁ : F₂ will be :

The refractive index of the material of a prism is $$\sqrt 2 $$ and the angle of the prism is 30°. One of the two refracting surfaces of the prism is made a mirror inwards, by silver coating. A beam of monochromatic light entering the prism from the other face will retrace its path (after reflection from the silvered surface) if its angle of incidence on the prism is

An object is placed at a distance of 40 cm from a concave mirror of focal length 15 cm. If the object is displaced through a distance of 20 cm towards the mirror, the displacement of the image will be

An astronomical refracting telescope will have large angular magnification and high angular resolution, when it has an objective lens of