A point source of light of power P and wavelength λ is emitting light in all directions. The number of photons present in a spherical region of radius ‘r’ to radius $$2r$$ with centre at source, is

Question

A point source of light  of power P and wavelength λ      is emitting light in  all directions. The number of photons present in a spherical region of radius  ‘r’ to radius $$2r$$ with centre at source, is

Infinity Learn · Accepted Answer

Intensity at a distance x from  point source is given by  $$I=P4$$$$π$$$$x2$$        consider an elemental shell of  radius x and thickness dx, in this region, the energy contained is $$dE=Ic$$×$$4$$$$π$$$$x2dx=Pdxc$$      Let dn be the number of photons in  this elemental shell, then dn×hcλ$$=dE=Pdxc$$               ⇒ $$dn=P$$λ$$dxhc2$$     Total no.of photons in the shell of inner radius r and  outer radius $$2r$$ is $$n=$$∫$$dn=$$∫$$r2rP$$λ$$dxhc2=P$$λ$$rhc2$$

A point source of light of power P and wavelength $λ$ is emitting light in all directions. The number of photons present in a spherical region of radius ‘r’ to radius 2r with centre at source, is

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A point source of light of power P and wavelength λ is emitting light in all directions. The number of photons present in a spherical region of radius ‘r’ to radius 2r with centre at source, is

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A point source of light of power P and wavelength $λ$ is emitting light in all directions. The number of photons present in a spherical region of radius ‘r’ to radius 2r with centre at source, is