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## QuestionPhysicsClass 12

The intensity of light pulse travelling in an optical fiber decreases according to the relation $${I}={I}_{{{0}}}{e}^{{-\alpha{x}}}$$ . The intensity of light is reduced to $${20}\%$$ of its initial value after a distance x equal to
(A) In$${\left(\frac{{{1}}}{{\alpha}}\right)}$$
(B) In$${\left(\alpha\right)}$$
(C) $$\frac{{{\left(\text{In}{5}\right)}}}{{\alpha}}$$
(D) In $${\left(\frac{{{5}}}{{\alpha}}\right)}$$

$$\frac{{{I}}}{{{I}_{{{0}}}}}={e}^{{-\alpha{x}}}=\frac{{{20}}}{{{100}}}={e}^{{\alpha{x}}}={5}$$
$${a}{x}={{\log}_{{{e}}}{5}},{x}=\frac{{{\left(\text{In}{5}\right)}}}{{\alpha}}$$
OR
$${I}={I}_{{{0}}}{e}^{{-\alpha{x}}}$$
$${0.2}{I}_{{{0}}}={I}_{{{0}}}{e}^{{-\alpha{x}}}$$
$$\frac{{{2}}}{{{10}}}={e}^{{-\alpha{x}}}\Rightarrow\frac{{{10}}}{{{2}}}={e}^{{\alpha{x}}}$$
$${l}{n}{\left({5}\right)}={\left.{d}{x}\right.}$$
$${x}=\frac{{{l}{n}{\left({5}\right)}{J}}}{{\alpha}}$$