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Question

A light of wavelength 6000˚A shines on two narrow slits separated by a distance 1.0mm and illuminates a screen at a distance 1.5m away. When one slit is covered by a thin glass plate of refractive index 1.8 and other slit by a thin glass plate of refractive index μ, the central maxima shifts by 0.1rad. Both plates have the same thickness of 0.5mm. The value of refractive index μ of glass is:

A
1.4
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B
1.5
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C
1.6
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D
none of these
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Solution

The correct option is B 1.6
Lateral shift ¯¯¯¯¯X=Dd(μ1)t and tanθθ=¯¯¯¯¯XD
Central maxima shift Δθ=td[(1.81)(μ1)]=td(1.8μ)
Refractive index of glass μ=1.8Δθdt=1.80.1×10.5=1.80.2=1.6

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