Question

a slit has two slots. A monochromatic light of 450nm passes by the two slots. you can observe in a screen that the distance between the third and the sixth dark strip is 4.50x10^2 m. If the screen is 2.50m from the slit. Determine the separation between the slits.

Answer 1

For destrutive or dark strip

Path difference = dy/D = (2n -1 )* Y/2

y = ( 2n -1 )*D*Y/2d - equation (1)

,where n= 1,2,3 ,.............

here y is the distance of drak fringe from central bright fringe , Y is the wavelength of monochromatic light used it's value is given Y =  450nm = 450 x 10-9 m  , D is the distance between slit and the screen and it is given D = 2.50m ,d is distance between the slits .

The distance between the third and the sixth dark strip is given 4.50 x102 m.

For sixth dark strip in equation 1

n = 6

y6 = ( 2*6 - 1) *D*Y/2d

For third dark strip in equation 1

n = 3

y3 = ( 2*3 - 1) *D*Y/2d

y6 -      y3 = ( 2*6 - 1) *D*Y/2d - ( 2*3 - 1) *D*Y/2d

y6 -      y3 = ( 11) *D*Y/2d - ( 5) *D*Y/2d      

4.50 x102 = [ 11 - 5]  *D*Y/2d

  4.50 x102 = [ 6 ]  *2.50 * 450 x 10-9/2d

d= 7.5 x 10 -9  m

distance between the slits ,d = 7.5 x 10 -9  m or 7.5 nm