The eye can detect 5 ×10^4 photons per square metre per sec of gr… - Vidyadip

MCQ

The eye can detect $5 ×10^4$ photons per square metre per sec of green light ($\lambda$ $= 5000\ \mathop A\limits^o $) 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

✓
$5$
B
$10$
C
$106$
D
$1539$

✓

Answer

Correct option: A.

$5$

a
(a) $E = \frac{{12375}}{{5000}} = 2.475\,eV\, \approx 4 \times {10^{ - 19}}J$

So the minimum intensity to which the eye can respond

${I_{Eye}} = $ (Photon flux) $×$ (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.

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