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. Statement I is True, statement II is True, Statement II is a correct explanation for Statement I.
B. Statement I is Ture, Statement II is Ture, Statement II is NOT a correct explanation for Statement I.
C. Statement I is True, Statement II is False.
D. Statement I is False, Statement II is True.

Answer

b

Explanation

For two coherent sources,
`I = I_(1) + I_(2) + sqrt(I_(1) I_(2)) cos theta`
Putting `I_(1) = I_(2) = I_(0)`, we have
`I = I_(0) + I_(0) + 2 sqrt(I_(0) xx I_(0)) cos phi`
Simplifying the aboe expression,
`I = 2 I_(0) (1 + cos phi)`
`= 2 I_(0) (1 + 2 cos^(2) ((phi)/(2) - 1)`
`= 2 I_(0) xx cos^(2) ((phi)/(2)) = 4 I_(0) cos^(2) ((phi)/(2))`
Also,
`I_(max) - (sqrtI_(1) + sqrtI_(2))^(2)`
`I_(min) = (sqrt I_(1) + sqrt I_(2))`
`:. (I_(max))/(I_(min)) = ((sqrt I_(1) + sqrt I_(2)))/((sqrt I_(1) - sqrt I_(2)))`.