Question

In a Young's double-slit experiment, a set of parallel slits with a separation of 0.126 mm is illuminated by light having a wavelength of 571 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 fourth order bright fringe on the screen?
μm

(b) What is the difference in path lengths from the two slits to the location of the fourth dark fringe on the screen, away from the center of the pattern?
μm

Answer 1

(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 so on.
In general d = ml for an mth order fringe.
For the fourth order bright fringe, d = 4l
= 4(571nm)
= 2284nm = 2.284µm.

(b) The first dark fringe occurs where the path lengths differ by half a wavelength (destructive interference). The mth dark fringe occurs where d = (m + ½)l. At the fourth dark fringe, d = 4.5l
= 4.5(571nm)
= 2570 nm
= 2.57 µm.