In a double slit experiment, the intensity of light at the center of the central bright fringe is measured to be 6.2 µW/m². What is the intensity halfway between the center of this fringe and the first dark band, assuming that the small-angle approximation is valid? A) 6.2 µW/m² B) 3.1 µW/m² C) 4.7 µW/m² D) 1.6 µW/m² E) 0.12 µW/m²

Question

Quizplus · Accepted Answer

According to the small-angle approximation, the angle between the center of the central bright fringe and the first dark band is given by:

θ ≈ λ/d,

where λ is the wavelength of light and d is the distance between the two slits. The distance between the center of the central bright fringe and the first dark band is half the distance between two consecutive bright fringes, which is given by:

y ≈ λD/d,

where D is the distance between the double slit and the screen. Therefore, the intensity halfway between the center of the central bright fringe and the first dark band is:

I ≈ I0/4,

where I0 is the intensity at the center of the central bright fringe. Hence, we have:

I ≈ 6.2 µW/m  / 4 ≈ 1.55 µW/m.

Therefore, the best choice is B.

In a Double Slit Experiment, the Intensity of Light at the Center