Question

Two slits spaced 0.130 mm apart are placed 90.0 cm from a screen and illuminated by coherent light with wave length 550 nm. the intensity at the center of the central maximum ( degrees) is 4.00 X 10^-6 W/m² A) what is the distance on the screen from the center of the central maximum to the first minimum? B) what is the intenisty at a point midway between the center of the central maximum and the first minimum?

Answer 1

Two slits spaced (2d) = 0.130 mm =0.130*10^-3m

The distance between the slits and screen is (D) = 90.0 cm =0.9m

The illuminated by coherent light with wave length (lamda) = 550 nm =550*10^-9m.

The intensity at the center of the central maximum ($\theta =0$ degrees) is (I) =4.00 X 10^-6 W/m²

For a first dark fringe i.e fo the first minima

                                    xn =(D/2d)(2n+1)lamda/2      for firstminima n=1

now the distance on the screen from the center of the central maximum to the first minimum

                                   xn =(D/2d)*(2n+1)lamda/2 =(0.9/0.130*10^-3m)(3)*550*10^-9m/2 =571.15*10^-6 =5.711mm

At the mid point means

                                    xn =2.855mm