A Young's double slit experiment is performed in air using a monochromatic light source, and 12 fringes are observed in a specific field of view on the screen. If the entire apparatus is subsequently immersed in a transparent liquid of refractive index 4 3 without changing the light source or the geometry, how many fringes will now be observed in the same field of view?

Step-by-step solution

The fringe width in air is = D d . The length of the field of view containing n fringes is y = n = n D d . When the apparatus is immersed in a liquid of refractive index , the wavelength of light in the liquid becomes ' = . Since the field of view y remains the same, the new number of fringes n' is given by y = n' ' D d . Equating the two expressions for y gives n = n' ' . Substituting ' = , we get n = n' ( ) , which simplifies to n' = n . Given n = 12 and = 4 3 , the new number of fringes is n' = 12 4 3 = 16 . Ans