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 ra

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 r + x with centre at the source is hc 2 nP λ x ​ . Find the value of n ?

TestHub · Accepted Answer

The energy stored in the spherical region between r and $r + x$ is

$=$ energy density $\times 4 π r^{2} dx = \frac{I}{c} \times 4 π r^{2} dx = \frac{P}{4 π r ^{2} c} 4 π r^{2} dx = \frac{Pdx}{c}$

∴ Number of photons in the given volume is $= \frac{Pdx}{hvc} = \frac{P λ dx}{hc ^{2}}$

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