Question

Two slits spaced 0.400 mm apart are placed 72.0 cm from a screen.

Part A

What is the distance between the second and third dark lines of the interference pattern on the screen when the slits are illuminated with coherent light with a wavelength of 530 nm ? (delta y=_in mm)

Answer 1

Y₂ = Position of second dark line

Y₃ = Position of third dark line

d = slit spacing = 0.4 x 10^-3 m

D = screen distance = 0.72 m

= wavelength = 530 nm = 530 x 10^-9 m

position of second dark line is given as

Y₂ = (2n - 1) D/2d = (2 x 2 - 1) (0.72) (530 x 10^-9 ) /(2 x 0.4 x 10^-3 ) = 0.00143

position of third dark line is given as

Y₃ = (2n - 1) D/2d = (2 x 3 - 1) (0.72) (530 x 10^-9 ) /(2 x 0.4 x 10^-3 ) = 0.00239

Y = Y₃ - Y₂ = 0.00239 - 0.00143 = 0.00096 m = 0.96 mm