Question

in youngs double slit experiment the width of the fringes obtained withy ligh of wavelength 5500 angstrom is 3.9mm. calculate the fringe width if the entire apparatus is immersed in a liquid medium of refractive index 1.3

Answer 1

In Young's double slit experiment :

     β = fringe width = λ D / d,
                     D = perpendicular distance between slits and screen
                     λ = wavelength of light source,
                     d = distance between slits

     velocity in vacuum / velocity in liquid = 1.3
       λ  in vacuum * frequency / λ in liquid * frequency  = 1.3
             λ in liquid = 5,500 / 1.3  Angstroms
  
       β is proportional to λ , as D and d are same.

         β in vacuum / β liquid medium  = λ in vacuum / λ in liquid

             β in liquid =  β in vacuum * λ in liquid / λ in vacuum
                             = 3.9 mm * (5,500 /1.3) Angstrom / (5,500 Angstrom)
                             = 3.9 / 1.3 =  3 mm