In Young's double slit experiment, the separation between two slits is 0.3 10⁻³ ~m . When light beam is passed through the two slits, then interference pattern is observed on the screen 1.5 m away. If the first violet and red fringes are formed 2.0 mm and 3.5 mm away from the central white fringe, then the difference in wavelength of red and violet light is x 10⁻⁹ ~m . The value of x is

Step-by-step solution

In a Young's double slit experiment for interference pattern, the position of bright fringe is given by y_n= n D d Here, aligned & D=1.5 ~m & d=0.3 10⁻³ ~m aligned and n=1 ; = y_n d D For first violet, y_n=2 ~mm =2 10⁻³ ~m _ violet =2 10⁻³ d D For first red, aligned y_n & =3.5 ~mm =3.5 10⁻³ ~m _ red & =3.5 10⁻³ d D aligned The difference in wavelengths of red and violet light is aligned & = _ red - _ violet & =3.5 10⁻³ d D -2 10⁻³ d D & = d D (1.5) 10⁻³ & = 0.3 10⁻³ 15 1.5 10⁻³ & =0.3 10⁻⁶=0.3 10⁻⁶ 10^3 10⁻³ & =300