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

Options

A. `ln (1/alpha)`
B. `ln (alpha)`
C. `((ln 5))/(alpha)`
D. `ln (5/alpha)`

Answer

C

Explanation

`I/(I_0) = e^(-alphax) = (20)/(100) implies e^(alpha x)= 5`
`alphax = log_e 5, x = ((ln 5))/(alpha)`
or
`I = I_0 e^(-alpha x)`
`0.2 I_0 = I_0 e^(-alphax)`
`2/10 = e^(-alpha x) implies 10/2 = e^(alpha x)`
`ln (5) = dx`
`x = (ln (5))/(alpha)`