Wave Optics

JEE Main level, numerical answer, medium

138 of 191

Question 138 of 191

The difference in the number of waves when yellow light propagates through air and vacuum columns of the same thickness is one. The thickness of the air column is _____ mmmm. [Refractive index of air =1.0003=1.0003, the wavelength of yellow light in vacuum =6000A∘]=6000A^{^{\circ}}]

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Answer: 2

Thickness t=nλt=n\lambda
So, nλvac=(n+1)λairn{\lambda }_{vac}=(n+1){\lambda }_{air}
nλ=(n+1)λμairn\lambda =(n+1)\dfrac{\lambda }{{\mu }_{air}}
n=1μair−1=1043n=\dfrac{1}{{\mu }_{air}-1}=\dfrac{{10}^{4}}{3}
t=nλt=n\lambda
=1043×6000A0=\dfrac{{10}^{4}}{3}\times 6000A^{0}
=2mm=2mm

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