In a YDSE experiment the two slits are covered with a transparent membrane of negligible thickness which allows light to pass through it but does not allow water. A glass slab of thickness t =0.41 ~mm and refractive index ₃=1.5 is placed infront of one of the slits as shown in the figure. The separation between the slits is d =0.30 ~mm . The entire space to the left of the slits is filled with water of refractive ind

Step-by-step solution

(a) Let central maxima lies at point P at a distance x from the central line. Then optical path difference p at point P is aligned & ( S ₂ P - t )+ t _ B - _ w ~d - S ₁ P & ~S ₂ P - S ₁ P + ( _B-1 ) t - _ w ~d & xd D + ( _ B -1 ) t - _ v ~d aligned For central maxima p =0 aligned x & = D d [ ( _w d )- ( _g-1 ) t ] & = 1 3 10⁻⁴ [ 4 3 3 10⁻⁴ 1 2 -0.5 0.41 10⁻³ ] & = 1 3 10⁻⁴ [2 10⁻⁴-2.05 10⁻⁴ ]=- 5 10⁻⁶ 3 10⁻⁴ & =-1.66 10⁻² ~m =-1.66 ~cm aligned Central maxima lies at a distance 1.66 cm below the central line