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  •  Minimum light intensity that can be perceived by normal human eye is about <img alt="10^{-10} \mathrm{Wbm}^{-2}." src="https://entrancecorner.oncodecogs.com/gif.latex?10%5E%7B-10%7D%20%5Cmath

 Minimum light intensity that can be perceived by normal human eye is about 10^{-10} \mathrm{Wbm}^{-2}. What is the minimum number of photons of wavelength 660 \mathrm{~nm} that must enter the pupil in 1 \mathrm{~s} for one to see the object?

Area of cross-section of the pupil is 10^{-4}m^{2}

Option: 1

3.3 \times 10^2


Option: 2

\quad 3.3 \times 10^3


Option: 3

3.3 \times 10^4


Option: 4

3.3 \times 10^5


Answers (1)

best_answer

Intensity, \mathrm{I}=10^{-10} \mathrm{Wbm}^{-2}=10^{-10} \mathrm{Js}^{-1} \mathrm{~m}^{-2}.

Let the number of photons required be \mathrm{n}.

Then, \mathrm{I}=\frac{\mathrm{nhv}}{\mathrm{A}}=\frac{\mathrm{nhv}}{10^{-4}}=10^{-10}

Hence, \mathrm{n}=10^{-10} \times 10^{-4} / \mathrm{hv}=10^{-14} \frac{\lambda}{\mathrm{hc}}

=\frac{10^{-14} \times 660 \times 10^{-9}}{6.6 \times 10^{-34} \times 3 \times 10^8}=3.3 \times 10^4

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