Q#34 (Past Exam Paper – June 2017 Paper 13 Q28)
Monochromatic light of wavelength λ is incident on two narrow slits S1 and S2, a small distance apart. A series of bright and dark fringes are observed on a screen a long distance away from the slits.
The n th dark fringe from the central bright fringe is observed at point P on the screen.
Which equation is correct for all positive values of n?
A S2P – S1P = nλ / 2
B S2P – S1P = nλ
C S2P – S1P = (n – ½)λ
D S2P – S1P = (n + ½)λ
Solution:
Answer: C.
Dark fringes are formed when destructive interference occurs.
For destructive interference, the path difference should be 0.5λ, 1.5λ, 2.5λ, 3.5λ … [B is incorrect]
Consider option A.
Path difference = nλ /2
When n = 1, path difference = ½ λ
When n = 2, path difference = 2 λ / 2 = λ [A is incorrect]
Consider option D.
When n = 1, path difference = (1 + ½) λ = 3λ / 2
This equation suggest that the first dark fringe occurs at 3λ / 2. [D is incorrect]
Consider option C.
When n = 1, path difference = (1 – ½) λ = λ / 2
This equation suggest that the path difference for the first dark fringe is equal to λ / 2 (= 0.5λ), which is correct.
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