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Question

In YDSE shown in figure, a parallel beam of light is incident on the slits from a medium of refractive index n1. The wavelength of light in this medium is λ1. 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 is n2. The phase difference between the light waves reaching point O (symmetrical, relative to the slits) is :

164541_be845e13ffe84e2792da772a0e36f07c.png

A
2πn1λ1(n3n2)t
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B
2πλ1(n3n2)t
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C
2πn1n2λ1(n3n21)t
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D
2πn1λ1(n3n2)t
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Solution

The correct option is A 2πn1λ1(n3n2)t
Path difference in air at point O Δx=[(S1Ot)n2+tn3(S2O)n2]=[(S1OS2O)n2+(n3n2)t]

Duetosymmetry,(S1OS2O)=0

Δx=(n3n2)t

Phase difference =2πn1λ× Path difference in air

Δϕ=2πn1λ×Δx=2πn1λ(n3n2)t

406638_164541_ans_bc1ceb7b54364d3b9198bb1c7fd7c13b.png

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