In the figure an arrangement of young's double slit experiment is shown. A parallel beam of light of wavelength ' λ ' (in medium n 1 ) is incident at an angle ' θ ' as shown. Distance S 1 O = S 2 O. Point 'O' is the origin of the coordinate system. The medium on the left and right side of the plane of slits has refractive index n 1 and n 2 respectively. Distance between the slits is d. The distance between the screen and the plane of slits is D. Using D = 1m, d = 1mm, θ = 30°, λ = 0.3mm, n 1 = 
, n 2 = 
, answer the following
(i) The y-coordinate of the point where the total phase difference between the interefering waves is zero, is
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(i) If phase difference at point P is zero then
n 1 d sin θ = n 2 d sin θ '
⇒ θ ' = 37°
and as tan θ ' = 
⇒ y = – 
m
It is negative because upper path in medium n 2 is longer than lower path in the same medium.
(ii) Path lengths in medium 2 are equal for point O. Therefore
path difference = d sin θ
, 
,
∴ Δφ = 
Δ p
= 
Ι = Ι 0 + Ι 0 + 2 Ι 0 
= Ι 0
(iii) As we go up from point O, path difference will increase. At O, phase difference is 3 π + 
and when it becomes 4 π , there will be maximum. Extra path difference created in medium 2 must lead to 
phase difference.
. d sin θ 1 . n 2 = 
Using values sin θ 1 = 
⇒ tan θ 1 = 
= 
y = 
cm = 
cm
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