Q120 / 120 · VITEEE 2014 · Physics

An eye can detect $5 \times 10^{4}$ photons per square meter per sec of green light $(\lambda \alpha=5000 Å)$ while the ear can detect $10^{-13} \mathrm{~W} / \mathrm{m}^{2}$. The factor by which the eye is more sensitive as a power detector then ear is close to

  • Correct answer
    A
    5
  • B
    10
  • C
    $10^{6}$
  • D
    15

Solution

Energy $=\frac{12375}{5000}=2.475 \mathrm{eV}=4 \times 10^{-19} \mathrm{~J}$ Minimum intensity to which the eye can respond. $\begin{array}{l} 1_{\text {eye }}=(\text { photon flux }) \times \text { energy of a photon } \\ 1_{\text {eye }}^{\text {fort }}=\left(5 \times 10^{4}\right) \times 4 \times 10^{-19} \\ =2 \times 10^{-14} \mathrm{~W} / \mathrm{m}^{2} \end{array}$ Now, lesser the intensity required by a detector for detection more sensitive it will $\mathrm{be}=\frac{\mathrm{l}_{\mathrm{ear}}}{\mathrm{l}_{\text {eye }}}=\frac{10^{-13}}{2 \times 10^{-14}}=5$

Hence, the correct answer is option: 'A'.

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