Question

Violet light $(\lambda =4000\mathring{A})$ of intensity $4watt/m^2$ falls normally on a surface of area $10cm\times 20cm$. Find
(a) the energy received by the surface per second,
(b) the number of photons hitting the surface per second,
(c) if surface is tilted such that plane of the surface makes an angle ${30}^o$ with light beam, find the number of photons hitting the surface per second.

Answer 1

(a) Energy received per second per unit area
$E=IA\cos \theta =4\times 0.02J=0.08J$.
(b) $nh\left(c/\lambda \right)=E$
$\Rightarrow n=\frac{0.08\times 4000\times {10}^{-10}}{6.63\times {10}^{-34}\times 3\times {10}^8}=\frac{32\times {10}^{17}}{19.89}=1.609\times {10}^{17}$
(c) $n=\frac{IA\cos {60}^o\times \lambda }{hc}=\frac{1}{2}\times \frac{32\times {10}^{17}}{19.89}=0.805\times {10}^{17}$.