As shown in figure waves with identical wavelengths and amplitudes and which are intially in phase travel through difference media. Ray 1 travels through air and Ray 2 through a transparent medium for equal length L, in four different situations. Rays reach a common point on the screen. The number of wavelengths in length L is `N_(2)` for Ray 2 and `N_(1)` for Ray 1. In the following table, values of `N_(1)` and `N_(2)` are given for all four situations. The order or the situations according to the intensity of the light at the common point in descending order is Situations
1 2 3 4
`N_(1)` 2.75 1.80 3.00 3.25
`N_(2)` 2.75 2.80 3.25 4.00

Options

A. `I_(3) = I_(4) gt I_(2) gt I_(1)`
B. `I_(1) gt I_(3) = gt I_(4) gt I_(2)`
C. `I_(1) gt I_(2) gt I_(3) gt I_(4)`
D. `I_(2) gt I_(3) = I_(4) gt I_(1)`

Answer

d

Explanation

In cases, I, II, III and IV, the path difference are respectively,
`(lambda)/(2) , lambda, (lambda)/(4)` and `(3 lambda)/(2)`
Phase difference are, respectively, `pi, 2pi, (pi)/(2) , (3 pi)/(2)`, and
`I = I_(0) cos^(2) ((phi)/(2))`
Therefore, the intensities in the four cases are 0, `I_(0), (I_(0))/(2), (I_(0))/(2)`,respectively.