Monochromatic light of wavelength `5000 Å` is used in YDSE, with slit width, `d = 1 mm`, distance between screen and slits, `D = 1 M`. If intensites at the two slits are `I_1 = 4I_0 and I_2 = I_0`, find:
a. finge width `beta:`
b. distance of 5th minima from the central maxima on the screen,
c. intensity at `y = (1)/(3) mm,`
d. distance of the 1000th maxima, and
e. distance of the 5000th maxima.

Explanation

At `y=(1)/(3)mm`
`y lt lt D`
Hence `Delta p = (dy)/(D)`
`Delta phi = (2pi)/(lambda)`
`Delta p = 2pi (dy)/(lambda D)=(4pi)/(3)`
Now resultant intensity
`I=I_(1)+I_(2)+2sqrt(I_(1)I_(2))cos Delta phi`
`= 4I_(0)+I_(0)+2sqrt(4I_(0)^(2))cos Delta phi`
`= 5I_(0)+4I_(0)"cos"(4pi)/(3)=3I_(0)`