Statement I: In Young's experiment, for two coherent sources, the resultant intensity is given by `I = 4 I_(0) cos^(2) ((phi)/(2))`
Statement II: Ratio of maixmum to minimum intensity is `(I_(max))/(I_(min)) = ((sqrt I_(1) + sqrt I_(2))^(2))/((sqrt I_(2) - sqrt I_(2))^(2))`.

Options

A. (a) If both assertion and reason are true and reason is the correct explanation of assertion.
B. (b) If both assertion and reason are true but reason is not the correct explanation of assertion.
C. (c) If assertion is true but reason is false.
D. (d) If assertion and reason both are false.

Answer

B

Explanation

For two coherent sources,
`I=I_1+I_2+sqrt(I_1I_2)costheta`
Putting, `I_1=I_2=I_0`
We have `I=I_0+I_0+2sqrt(I_0xxI_0)cosvarphi`
Simplifying the above expression
`I=2I_0(1+cos varphi)`
`=2I_0(1+2co s^2varphi/2-1)`
`=2I_0xx2cos^2varphi/2=4I_0co s^2varphi/2`
Also, `I_(max)=(sqrt(I_1)+sqrt(I_2))^2`
`I_(min)=(sqrt(I_1)+sqrt(I_2))`
`:. I_(max)/I_(min)=((sqrt(I_1)+sqrt(I_2))^2)/((sqrt(I_1)-sqrt(I_2))^2)`