In a Young\'s double-slit experiment, a set of parallel slits with a separation
ID: 1450802 • Letter: I
Question
In a Young's double-slit experiment, a set of parallel slits with a separation of 0.122 mm is illuminated by light having a wavelength of 591 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 third order bright fringe on the screen?
=? m
(b) What is the difference in path lengths from the two slits to the location of the third dark fringe on the screen, away from the center of the pattern?
=?m
thankyou :)
Explanation / Answer
( a)
In general d = m for an mth order fringe.
For the third order bright fringe,
d = 3 = 3(591 nm) = 1773 nm = 1.773 µm.
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( b )
First dark fringe occurs where the path lengths differ by half a wavelength (destructive interference).
The mth dark fringe occurs where d = (m + ½)
At the third dark fringe,
d = 3.5= 3.5(591 nm) = 2068.5 nm = 2.0685 µm.