On a hot summer night, the refractive index of air is smallest near the ground and increases with height from the ground. When a light beam is directed horizontally, the Huygens' principle leads us to conclude that as it travels, the light beam :

Assuming human pupil to have a radius of $$0.25$$ $$cm$$ and a comfortable viewing distance of $$25$$ $$cm$$, the minimum separation between two objects that human eye can resolve at $$500$$ $$nm$$ wavelength is :

Two beams, $$A$$ and $$B$$, of plane polarized light with mutually perpendicular planes of polarization are seen through a polaroid. From the position when the beam $$A$$ has maximum intensity (and beam $$B$$ has zero intensity), a rotation of polaroid through $${30^ \circ }$$ makes the two beams appear equally bright. If the initial intensities of the two beams are $${{\rm I}_A}$$ and $${{\rm I}_B}$$ respectively, then $${{{{\rm I}_A}} \over {{{\rm I}_B}}}$$ equals:

A beam of unpolarised light of intensity $${{\rm I}_0}$$ is passed through a polaroid $$A$$ and then through another polaroid $$B$$ which is oriented so that its principal plane makes an angle of $${45^ \circ }$$ relative to that of $$A$$. The intensity of the emergent light is