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

A thin prism having refracting angle 10^o is made of glass of refractive infex 1.42. This prism is combined with another thin prism of glass of refractive index 1.7. This combination producess dispersion without deviation. The refracting angle of second prism should be