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A 0.6 \times 10^{-3} W laser is aimed at the Moon. The wavelength of emitted light is 600 \mathrm{~nm} and the laser beam spreads out of the source at a divergence angle of \theta=0.5 \times 10^{-3} \mathrm{rad}. The Earth-Moon distance is nearly 4 \times 10^8 \mathrm{~m}. Calculate the maximum number of photons arriving per second per square meter on the Moon? Neglect any absorption by the atmosphere.

Option: 1

\begin{aligned} & 5.7 \times 10^4 \mathrm{~m}^{-2} \mathrm{~s}^{-1} \\ \end{aligned}


Option: 2

\begin{aligned} & 10.7 \times 10^4 \mathrm{~m}^{-2} \mathrm{~s}^{-1} \\ \end{aligned}


Option: 3

\begin{aligned} & 10.14 \times 10^4 \mathrm{~m}^{-2} \mathrm{~s}^{-1} \\ \end{aligned}


Option: 4

\begin{aligned} & 5.14 \times 10^6 \mathrm{~m}^{-2} \mathrm{~s}^{-1} \end{aligned}


Answers (1)

best_answer

Number of photons emitted (per second) from the source is

 

Beam diameter

\begin{aligned} d & =r \theta=4 \times 10^8 \times 0.5 \times 10^{-3} \\ \\& =2 \times 10^5 \mathrm{~m} \end{aligned}

Area illuminated on the moon 

\begin{aligned} A & =\pi\left(\frac{d^2}{4}\right) \\ \\& =3.14 \times \frac{4 \times 10^{10}}{4}=3.14 \times 10^{10} \mathrm{~m}^2 \end{aligned}

\thereforeNumber of photons incident per unit area per second

=\frac{1.8 \times 10^{15}}{3.14 \times 10^{10}}=5.7 \times 10^4 \mathrm{~m}^{-2} \mathrm{~s}^{-1}

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vinayak

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