In Young's double slit experiment, the width of the fringes obtained with light of wavelength \( 6000\,\mathring{\mathrm{A}} \) is 3.0 mm. If the entire apparatus is immersed in a liquid medium of refractive index 1.50, then the fringe width would be
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 2.0 mm
The fringe width is \( \beta = \lambda D/d \). In a liquid of refractive index \( \mu \) the frequency stays the same but the wavelength decreases to \( \lambda/\mu \), while \( D \) and \( d \) are unchanged.
\( \displaystyle \beta' = \frac{\lambda D}{\mu\,d} = \frac{\beta}{\mu} \)
\( \displaystyle \beta' = \frac{3.0\,\mathrm{mm}}{1.50} = 2.0\,\mathrm{mm} \)
The wavelength 6000 Å is not needed, because only the ratio enters.