A source S is kept directly behind the slit S 1 in a double − slit apparatus. Find the phase difference at a point O which is equidistant from S 1 & S 2 . What will be the phase difference at P if a liquid of refraction index μ is filled; (wavelength of light in air is λ due to the source). Assume same intensity due to S 1 and S 2 on screen and position at liquid. ( λ << d, d << D, λ >> d
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
Δ φ = 
Δ φ = 
; D min = 
= 
Sol. 
at O; path difference
= dsin θ where θ is the angle as shown: (as λ >> d)
so , Δ P= d sin θ ≅ d tan θ ≈ 
= 
⇒ Δφ = 
= 
.
Now if a liquid is filled as shown.
path difference = (SS 2 – SS 1 ) + S 2 P – S 1 P
= 
+ 
⇒ phase difference = 
+ 
= 
(i) if liquid is filled on the left side.
Δφ = 
+ 
= 
(ii) Clearly it is asking about β /2 { λ << d}.
⇒ D min = 
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