JEE Advanced 2022 Paper 1 · Physics · Waves and Sound · medium

In a Young's double-slit experiment the entire apparatus is immersed in water of refractive index 4/3. A thin transparent film of refractive index…

Numerical answer

In a Young's double-slit experiment the entire apparatus is immersed in water of refractive index

4/3

. A thin transparent film of refractive index

1.5

and thickness

24\ \mu\mathrm{m}

is placed in front of one slit. The wavelength of the source in vacuum is

600\ \mathrm{nm}

. The number of fringes by which the central maximum shifts is ______ . Give the answer correct to two decimal places.

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Answer: 6.67

Optical path through the film exceeds that through the same thickness of water by

(\mu_f-\mu_w)t=(1.5-\tfrac43)\times24\ \mu\mathrm{m}=4\ \mu\mathrm{m}

. A path difference of one vacuum wavelength corresponds to one fringe (the optical path difference is what sets the phase), so the shift in fringes is

\dfrac{4\times10^{-6}}{600\times10^{-9}}=6.67

. The water only matters through the reduced path excess; the fringe width itself cancels out.

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