Q17 of 805 Page 1

In a double slit experiment, the distance between the slits is 3 mm and the slits are 2 m away from the screen. Two interference patterns can be seen on the screen one due to light with wavelength 480 nm, and the other due to light with wavelength 600 nm. What is the separation on the screen between the fifth order bright fringes of the two interference patterns?

Given :


Distance between the slits (d) = 3 mm


The distance between the slits and the screen (D) = 2m



By the principle of interference, condition for constructive interference is the path difference = nλ


xd/D = nλ


where x = distance of the bright fringe from the centre of the central bright fringe.


From the above formula


x = (D/d)nλ


5th bright fringe due to 480nm wavelength,


Putting the values in the above formula, we get



x1 = 1.6 × 10-3 m


= 1.6 mm


5th bright fringe due to 600 nm wavelength


x2 = 2 × 10-3 m


= 2 mm


Distance between 5th order bright fringe due to the two wavelengths is (x2 - x1) = (2-1.6) = 0.4 mm.


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