Monochromatic light of wavelength λ is incident on two narrow slits S1 and S2, a small distance apart

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.