In young's double slit experiment using monochromatic light of wavelengths `lambda`, the intensity of light at a point on the screen with path difference `lambda` is M units. The intensity of light at a point where path difference is `lambda//3` is

Options

A. `(M)/(2)`
B. `(M)/(4)`
C. `(M)/(8)`
D. `(M)/(16)`

Answer

B

Explanation

Resultant intensity
`I_(R)=I_(1)+I_(2)+2sqrt(I_(1)I_(2))costheta`
If path difference `=lambda`, phase difference `2pi`
`I_(R)=I+I+2sqrt(IxxI)cos2pi=4I=M " "( :' I_(1)=I_(2)=I) `
If path difference `(lambda)/(3)`, phase difference `phi = (2pi)/(3)`rad
`I_(R)^(')=I+I+2sqrt(IxxI)"cos"(2pi)/(3)=I=(M)/(4)`