In a YDSE two thin transparent sheets are used in front of the slits S₁ and S₂ ₁=1.6 and ₂=1.4 . If both sheets have thickness ' t ', the central maximum is observed at a distance of 5 mm from centre O . Now the sheets are replaced by two sheets of same material of refractive index ₁+ ₂ 2 but having thickness t₁ and t₂ such that ' t ' = t₁+t₂ 2 . Now central maximum is observed at distance of 8 mm from centre O on th

Step-by-step solution

x = ( S ₂ P - t ₂ )+ ₂ t ₂ - ( S ₁ P - t ₁ )+ ₁ t ₁ = ( S ₂ P - S ₁ P )+ ( ₂-1 ) t ₂- ( ₁-1 ) t ₁ (i) In first case : aligned & y ₁= D ~d t ( ₁-1 )- t ( ₂-1 ) = D ~d t ( ₁- ₂ ) & or t = 5 10⁻³ 1 10⁻³ 1 (1.6-1.4) & t ₁+ t ₂=5 10⁻⁵ aligned ......(A) (ii) When both sheets have same refractive index aligned & = 1.6+1.4 2 =1.5 & y ₂= D ~d t ₁( -1)- t ₂( -1) = D ~d ( -1) ( t ₁- t ₂ ) & t ₁- t ₂= 8 10⁻³ 1 10⁻³ 1 (1.5-1) = 8 10⁻⁶ 0.5 =1.6 10⁻⁵ aligned ......(B) On solving, t ₁=33 ~m