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. In`((1)/(alpha))`
B. In`(alpha)`
C. `(("In"5))/(alpha)`
D. In `((5)/(alpha))`

Answer

C

Explanation

`(I)/(I_(0)) = e^(-alpha x) = (20)/(100) = e^(alpha x) = 5`
`ax = log_(e) 5, x=(("In" 5))/(alpha)`
OR
`I=I_(0)e^(-alpha x)`
`0.2 I_(0) = I_(0) e^(-alpha x) `
`(2)/(10) = e^(-alpha x) rArr (10)/(2) = e^(alpha x)`
`l n(5) = dx`
`x=(l n(5)J)/(alpha) `