text: # In Young's double slit experiment, the fringe width is found to be 0.4 mm. If the whole apparatus is immersed in water of refractive index $$\dfrac{4}{3}$$, without disturbing the geometrical arrangement, the new fringe width will be
  
  1. 0.30 mm
  2. 0.40 mm
  3. 0.53 mm
  4. 450 microns
  
  Option 1 : 0.30 mm
  Free
  CT 1: हिन्दी (आदिकाल)
  6912
  10 Questions 40 Marks 10 Mins
  
  ## Detailed Solution
  
  Concept:
  
  Young’s Double Slit Experiment:
  
  If a monochromatic light falls on two narrow slits which are very close to each other act as a coherent source superpose each other and an interference pattern is observed on the screen.
  
  Property:
  
  • The central fringe is always bright as ϕ = 0°
  • If one slit is illuminated with red light and the other with green no pattern is observed.
  • All the fringes are of equal width β = λ D/d
  • Angular fringe width θ = λ /d
  • If the whole thing is submerged in water then βw = ¾ βa
  • Position of nth bright fringe from central maxima n = nλ d/D
  • Position of nth dark fringe from central maxima n = (2n-1)λ d/D
  
  Calculation:
  
  Fringe width in air (βa) = 0.4 mm
  
  We know that when submerged in water
  
  If the whole thing is submerged in water then:
  
  βw = ¾ βa
  
  βw = ¾ β= ¾ (0.4) = 0.3 mm