The eye can detect 5 x 10⁴ photons per square metre per sec of green light (λ = 5000 Å) while the ear can detect ${10^{ - 13}}\,(W/{m^2})$ . The factor by which the eye is more sensitive as a power detector than the ear is close to

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Detailed Solution

$E = \frac{{12375}}{{5000}} = 2.475\,eV\, \approx 4 \times {10^{ - 19}}J$
So the minimum intensity to which the eye can respond
I_Eye (Photon flux) x (Energy of a photon)
⇒ ${I_{Eye}} = (5 \times {10^4}) \times \,(4 \times {10^{ - 19}})\tilde --2 \times {10^{ - 14}}\,(W/{m^2})$
Now as lesser the intensity required by a detector for detection, more sensitive it will be
$\frac{{{S_{Eye}}}}{{{S_{Ear}}}} = \frac{{{I_{Ear}}}}{{{I_{Eye}}}} = \frac{{{{10}^{ - 13}}}}{{2 \times {{10}^{ - 14}}}} = 5$ i.e. as intensity (power) detector, the eye is five times more sensitive than ear