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 :

In total internal reflection when the angle of incidence is equal to the critical angle for the pair of media in contact, what will be angle of refraction?

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