Two coherent sources P and Q produce interference at point A on the screen where there is a dark band which is formed between 4th bright band and 5th bright band. Wavelength of light used is 6000 Å. The path difference between PA and QA is

Options

A. `1.4xx10^(-4)cm`
B. `2.7xx10^(-4)cm`
C. `4.5 xx 10^(-4)cm`
D. `6.2xx10^(-4)cm`

Answer

B

Explanation

According to question,
Path difference `Delta x` is given by `(lambda delta)/(2pi)`
[Where, `lambda=` wavelength of light, `delta=` phase difference]
For n=4th dark fringe,
`delta=(2n-1)pi`
`rArr delta=(8+1)pi=9pi`
`Delta x=(lambda9pi)/(2pi)=(9)/(2)lambda=(9)/(2)xx6xx10^(-7)`
`=2.7 xx 10^(-6)m=2.7xx10^(-4)cm`