In a Young\'s double-slit experiment, a set of parallel slits with a separation
ID: 2029262 • 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 556 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 fifth order bright fringe on the screen?
µm
(b) What is the difference in path lengths from the two slits to the location of the fifth dark fringe on the screen, away from the center of the pattern?
µm
Explanation / Answer
Given that, seperation between the slits, d = 0.102 mm = (0.102 mm)(1 x 10-3 m / 1 mm) = 0.102 x 10-3 m wavelength, = 556 nm = (556 nm)(1 x 10-9 m / 1 nm) = 556 x 10-9 m distance between the screen to slits, L = 4.50 m ______________________________________________________________________ ______________________________________________________________________ a) The difference in path lengths from the two slits to the location of a fifth order bright fringe on the screen is given by, r = m for the fifth order bright fringe, m = 5, then path difference, r = 5(556 x 10-9 m ) r = 2.78 m ______________________________________________________________________ ______________________________________________________________________ b) The difference in path lengths from the two slits to the location of the fifth dark fringe on the screen, away from the center of the pattern is given by, r = (m + (1/2)) For the fifth order dark fringe, m = 4, then path difference, r = (4 + (1/2))(556 x 10-9 m ) = (4 + 0.5)(556 x 10-9 m ) = (4.5)(556 x 10-9 m ) r = 2.502 mRelated Questions
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