In a Young\'s double-slit experiment, a set of parallel slits with a separation
ID: 1498631 • Letter: I
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 588 nm and the interference pattern observed on a screen 3.50 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? ____ µm
(b) What is the 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? ____ µm
Explanation / Answer
parallel slits with a separation of 0.102 mm
wavelength of 588 nm
pattern observed on a screen 3.50 m
(a) The zeroeth order bright fringe is where the path lengths are equal, at the first order fringe the path lengths differ by one wavelength (constructive interference), at the second order fringe the path lengths differ by two wavelengths, and at the second order fringe the path lengths differ by two wavelengths.
Path Difference = m*wavelength <---- Bright Fringe
In general d = m for an mth order fringe. For the second order bright fringe, d = 2 = 2(588nm) = 1176nm = 1.176µm.
(b) The first dark fringe occurs where the path lengths differ by half a wavelength (destructive interference).
Path Difference = (m + (1/2))*wavelength <---- Dark Fringe
The mth dark fringe occurs where d = (m + ½). At the second dark fringe,
d = 2.5 = 2.5(588nm) = 1470nm = 1.470µm.