An electromagnetic wave in vacuum has the electric and magnetic field $$\mathop E\limits^ \to $$and $$\mathop B\limits^ \to $$, which are always perpendicular to each other. The direction of polarization is given by $$\mathop X\limits^ \to $$ and that of wave propagation by $$\mathop k\limits^ \to $$. Then

An object $$2.4$$ $$m$$ in front of a lens forms a sharp image on a film $$12$$ $$cm$$ behind the lens. A glass plate $$1$$ $$cm$$ thick, of refractive index $$1.50$$ is interposed between lens and film with its plane faces parallel to film. At what distance (from lens) should object shifted to be in sharp focus of film?

Hydrogen atom is excited from ground state to another state with principal quantum number equal to $$4.$$ Then the number of spectral lines in the emission spectra will be :

A radar has a power of $$1kW$$ and is operating at a frequency of $$10$$ $$GHz.$$ It is located on a mountain top of height $$500$$ $$m.$$ The maximum distance upto which it can detect object located on the surface of the earth (Radius of earth $$ = 6.4 \times {10^6}m$$) is :