Question

In a Young's double-slit experiment, a set of parallel slits with a separation of 0.102 mm is illuminated by light having a wavelength of 600 nm and the interference pattern observed on a screen 4.50 m from the slits. (a) What is the difference in path lengths from the two slits to the location of a second order bright fringe on the screen?

Answer 1

Given

seperation between slits d = 0.102 nm

                                           = 0.102 * 10 ^-9 m

wave length of light   ?   = 600 nm

                                     = 600 *10 ^-9 m

distance between screen and slit   L = 4.5 m

  a) difference in path lengths from the two slits to the location of a second order bright fringe on the screen  

                   ? = d sin ? = m ?

for m =2  

                      ? = 2 ( 600 *10 ^-9 m )

                          = 1.200 ? m   

b) difference in path lengths from the two slits to the location of the second dark fringe on the screen, away from the center of the pattern

                   ? = ( m + 1/2 ) ?

                       = ( 2 + 1/2 )    ( 600 *10 ^-9 m )

                        = 1.500 ? m