Two narrow slits are illuminated by a laser with a wavelength of 522 nm. The interference pattern on a screen located x = 4.80 m away shows that the third-order bright fringe is located y = 9.10 cm away from the central bright fringe. Calculate the distance between the two slits.
The screen is now moved 0.9 m further away. What is the new distance between the central and the third-order bright fringe?
The position of the bright fringe is given by the equation
Where
n = order of fringe = 3
xn = position of n=3 fringe = 9.1 cm = 0.091 m
d = distance between the two slits
D = Distance between screen and slit = 4.8 m
= wavelength = 522 nm = 522 x
10-9 m
So, d = (3 x 522 x 10-9 x 4.8 )/0.091 m = 8.26 x 10-5 m
Now
New distance between the screen and slit = 4.8 + 0.9 m = 5.7 m
Hence, xn = (3 x 522 x 10-9 x 5.7 )/(8.26 x 10-5 ) m = 0.108 m
So,
Distance between the slits is 8.26 x 10-5 m -------------------(a)
New distance between central and third order fringe is 0.108 m ---------------------(b)
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