Two beams of light having intensities I and 4I interfere to produce a fringe pattern on the screen. Phase difference between the beams is $\frac{π}{2}$ at point a and $π$ at point B. Difference of intensities at A and B is

4 I

Given $I_1 = I, I_2 = 4I; θ_1=\frac{π}{2}$ and $θ_2=π$

$I_A = I_1 + I_2 + 2\sqrt{I_1I_2}\cos θ_1$

$I_1+I_2+2\sqrt{I_1I_2}\cos\frac{π}{2}=I_1 + I_2=5I$

$I_B = I_1 + I_2 + 2\sqrt{I_1I_2}\cos θ_2$

$= I_1 + I_2 + 2\sqrt{I_1I_2}\cos π=I$

$∴I_A-I_B=5I−I = 4I$