Two slits of width a = 0.020 mm are separated by a distance d = 0.05 mm and illuminated by light of wavelength λ = 500 nm. The number of bright fringes seen in the central maximum is
A) 2.5.
B) 3.
C) 4.
D) 5.
E) 6.

Question

Quizplus · Accepted Answer

The distance between the central maximum and the first bright fringe is given by:

sinθ ≈ θ ≈ λ/d

Thus, the angle between the central maximum and the first bright fringe is:

θ ≈ λ/d = (500 nm)/(0.05 mm) = 0.01 rad

The central maximum extends over an angle approximately given by:

Δθ ≈ a/d

Thus, the number of bright fringes within the central maximum is approximately:

N ≈ Δθ/θ = a/d ÷ λ/d ≈ a/λ

N ≈ (0.020 mm)/(500 nm) ≈ 40

However, since each bright fringe corresponds to a dark fringe as well, the actual number of bright fringes is half of this value.

Thus, N ≈ 20, and the closest option is C (4 bright fringes).

Two Slits of Width a = 0