Question

A 1 mW laser beam is incident onto a detector. Determine the fractional fluctuation in number of photons intercepted by the detector in a time interval T 1 us for photons with energy (a) E1 10 Me; (b) Ez 10 eV.

Answer 1

Answer:

(a) $625 photons$

(b)$625\times 10^{6}photons$

Explanation:

Given that , the power of the laser beam is,

$P=1 mW\\P=1\times 10^{-3} W$

and time is given is,

$t=1\mu s\\t=10^{-6}s$

Now the energy formula for the laser beam is,

$E=P\times t$

Now,

$E=10^{-3}\times 10^{-6} \\E=10^{-9}J$

(a) The value of energy is given,

$E_{1}=10MeV\\E_{1}=10\times 10^{6}\times 1.6\times 10^{-19}J\\ E_{1}=16\times 10^{-13}J$

Now the no of photons's fraction fluctuation is,

$n=\frac{E}{E_{1} }\\ n=\frac{10^{-9} }{16\times 10^{-13} }\\ E_{1}=625 photons$

Therefore the no of photons is $625 photons$.

(b)The value of energy is given,

$E_{z}=10eV\\E_{z}=16\times 10^{-19}J$

Now the no of photons's fraction fluctuation is,

$n=\frac{E}{E_{z} }\\ n=\frac{10^{-9} }{16\times 10^{-19} }\\n=625\times 10^{6}photons$

Therefore the no of photons is$625\times 10^{6}photons$.