3.  In the figure shown in a YDSE, a parallel beam of light is incident on the slits from a medium of refractive index n 1 .  The wavelength of light in this medium is λ 1 .  A transparent slab of thickness 't' and refractive index n3 is put in front of one slit.  The medium between the screen and the plane of the slits in n2 .  The phase difference between the light waves reaching point O (Symmetrical, relative to the slits) is:
A )     2 π n 1 λ 1 ( n 3 - n 2 )   t                     B )     2 π λ 1 n 3 - n 2   t                   C )     2 πn 1 n 2 λ 1 n 3 n 2 - 1 t                     D )     2 πn 1 λ 1 n 3 - n 2   t

Dear student,

Path difference in air at point Ox=S1O-tn2+tn3-S2On2tx=S1O-S2On2+n3-n2tx=(n3-n2)t as S1O=S2Ophase difference ϕ=2πλair(x)n1=λairλ1ϕ=2πn1λ1(n3-n2)t
So option (A) is correct
 
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