Young's double slit experiment is conducted with monochromatic light of wavelength 5000 Å , with slit separation of 3 ~mm and observer at 20 ~cm away from the slits. If a 1 ~mm transparent plate is placed infront of one of the slits, the fringes shift by 6 ~mm . The refractive index of the transparent plate is

Step-by-step solution

Given, wavelength, =5000 Å=5 10⁻⁷ ~m Slit separation, d=3 ~mm =3 10⁻³ ~m Distance between slit and screen, D=20 ~cm =0.2 ~m Thickness of transparent plate =1 ~mm =1 10⁻³ ~m Fringe shift, x=6 ~mm =6 10⁻³ ~m Fringe shift' is given by x= D d ( -1) t 6 10⁻³= 0.2 3 10⁻³ ( -1) 10⁻³ 6 3 10⁻³ 0.2 = -1 9 10⁻²= -1 =1.09 Hence, refractive index of transparent plate is 1.09 .