Consider the situation shown in figure. The two slits `S_1 and S_2` placed symmetrically around the central line are illuminated by a monochromatic light of wavelength `lamda`. The separation between the slits is d. The light transmitted by the slits falls on a screen `Sigma_1` placed at a distance D from the slits. The slit `S_3` is at the placed central line and the slit `S_4`, is at a distance z from `S_3`. Another screen`Sigma_2` is placed a further distance D away from 1,1. Find the ratio of the maximum to minimum intensity observed on `Sigma_2` if z is equal to a. `z=(lamdaD)/(2d)` b. `(lamdaD)/d` c. `(lamdaD)/(4d)`

Options

A. 4
B. 2
C. `oo`
D. 1

Answer

c

Explanation

`z = (lambda d)/(d)`
`Delta x` at `S_(4): Delta x = (lambda D)/(d) (d)/(D) = lambda`
Hence, maxima at `S_(4)` as well as `S_(3)`
Resultant intensity at `S_(4). I = 4 I_(0)`
`:. (I_(max))/(I_(min)) = ([(4 I_(0))^(1//2) + (4 I_(0))^(1//2)]^(2))/([(4 I_(0))^(1//2) - (4 I_(0))^(1//2)]^(2) )= oo`