A sensor is exposed for time t to a lamp of p | vedclass

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Question

Energy emitted by the $\operatorname{lamp}$ in time $t=P t$ where $P$ is the power of the $\operatorname{lamp}$ If $2 \mathrm{d}$ is radius of the sph

Vedclass · Accepted Answer

$\frac{{P\lambda {d^2}t}}{{hc{l^2}}}$

Vedclass · Answer

Energy emitted by the $\operatorname{lamp}$ in time $t=P t$ where $P$ is the power of the $\operatorname{lamp}$ If $2 \mathrm{d}$ is radius of the sphere and $l$ is the distance of source, then the energy reaching the sphere.

${m{E}} = \frac{{{m{Pt}}}}{{4\pi {l^2}}}\pi {(2{m{d}})^2}$

${m{E}} = \frac{{{m{Pt}}{{m{d}}^2}}}{{{l^2}}}$

$\frac{{{m{nhc}}}}{\lambda } \Rightarrow \frac{{{m{Pt}}{{m{d}}^2}}}{{{l^2}}}$

${m{n}} = \frac{{{m{Pt}}{{m{d}}^2}}}{{{l^2}}} 	imes \frac{\lambda }{{{m{hc}}}}\quad  \Rightarrow {m{n}} = \frac{{{m{Pt}}\lambda {{m{d}}^2}}}{{{m{hc}}{{m{l}}^2}}}$

A sensor is exposed for time $t$ to a lamp of power $P$ placed at a distance $l$. The sensor has a circular opening that is $4d$ in diameter. Assuming all energy of the lamp is given off as light, the number of photons entering the sensor if the wavelength of light is $\lambda $ is $(l >> d)$

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