Respuesta :
Answer:
Thus, the minimum number of photons per second is 77.34
Explanation:
Light intensity, [tex]I_{min}[/tex] = [tex]5\times 10^{-13} W/m^{2}[/tex]
Pupil has a diameter, d = 8.5 mm
= 8.5 x [tex]10^{-3}[/tex] m
Radius of the eye, r = 4.25 x [tex]10^{-3}[/tex] m
∴ Area of the eye, A = [tex]\pi .r^{2}[/tex]
= [tex]3.14\times \left ( 4.25\times 10^{-3} \right )^{2}[/tex]
= [tex]5.6\times 10^{-5} m^{2}[/tex]
Let [tex]P_{min}[/tex] be the minimum number of photons.
Therefore, [tex]P_{min}[/tex] = [tex]I_{min}[/tex] x A
= [tex]5\times 10^{-13}[/tex] x [tex]5.6\times 10^{-5}[/tex]
= [tex]2.8\times 10^{-17}[/tex] W
Thus the minimum number of photons is given by
[tex]N_{min}=P_{min}/E[/tex]
where E = [tex]hc/\lambda[/tex]
= [tex]\left (6.63\times 10^{-34}\times 3\times 10^{8} \right )/548\times 10^{-9}[/tex]
= [tex]3.62\times 10^{-19} J[/tex]
Therefore, [tex]N_{min}[/tex] = [tex]\frac{2.8\times 10^{-17}}{3.62\times 10^{-19}}[/tex]
= 77.34 photons per second
Thus, the minimum number of photons per second is 77.34
