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A two-slit interference experiment uses coherent light of wavelength 5 x 10^-7 m. Intensity in the interference pattern for the following points are $I_{1}, I_{2}, I_{3}, and I_{4}$ respectively.
1. A point that is close to one slit than the other by 5 x 10^-7 m.
2. A point where the light waves received from the two slits are out of phase by $\frac{4 π}{3} rad$ .
3. A point that is closer to one slit than the other by $7 .5 \times 10^{- 7} m$ .
4. A point where the light waves received by the two slits are out of phase by $\frac{π}{3} rad$ .
Then which of following statements is/are correct?

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$I_{1} > I_{4} > I_{3} > I_{2}$

$I_{1} > I_{4} > I_{2} > I_{3}$

$3 I_{2} = I_{4}$

$I_{3} = 0$

answer is B, C, D.

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Detailed Solution

$I = I_{0} \cos^{2} \frac{(πdsinθ)}{λ}$

(1) Path difference, $δ = dsin θ = 5 \times 10^{- 7} m$

$I_{1} = I_{0} \cos^{2} \frac{(π \times 5 \times 10^{- 7})}{(5 \times 10^{- 7} m)} = I_{0} \cos^{2} (π) = I_{0}$

(2) $I_{2} = I_{0} \cos^{2} (\frac{4 π}{2 \times 3} rad) = I_{0} \cos^{2} (\frac{4 π}{6}) = 0 .25 I_{0}$

$\begin{array}{l} (3) I_{3} = I_{0} \cos^{2} (\frac{π \times 7 .5 \times 10^{- 7} m}{5 \times 10^{- 7} m}) \\ = I_{0} \cos^{2} (1 .5 πrad) = I_{0} \cos^{2} (270^{\circ}) = 0 \end{array}$

$(4) I_{4} = I_{0} \cos^{2} (\frac{π}{2 \times 3}) rad = 0 .75 I_{0}$

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