Two beam of light having intensities I and 4I interfere to produce a fringe pattern on a screen. The phase difference between the beams is `(pi)/(2)` at point A and `pi` at point B. Then the difference between resultant intensities at A and B is : `(2001 , 2M)`

Options

A. 2I
B. 4I
C. 5I
D. 7I

Answer

B

Explanation

The resultant intensity `I=I_(1)+I_(2)+2sqrt(I_(1)I_(2))cosphi` . . . (1)
In this problem, `I_(1)=I,I_(2)=4I`
At point A, `phi=pi//2`
`therefore`From (1), `I_(A)=1+4I+2sqrt(4xx1)xxcos90^(@)`
`I_(A)=5I+0=5I`
At point B, `phi=180^(@)" "therefore cos180^(@)=-1`
`therefore I_(B)=I+4I+2xxsqrt(4xx1)cos180^(@)`
`=I+4I-4I=I`
`therefore I_(A)-I_(B)=5I-I=4I`