Question

In a classroom demonstration, a beam of coherent light of wavelength 550 nm is incident perpendicularly onto a pair of slits. Each slit has a width w of 1.2 x 10^–6 m, and the distance d between the centers of the slits is 1.8 x 10^–5 m. The class observes light and dark fringes on a screen that is a distance L of 2.2 m from the slits. Your notebook shows the following setup for the demonstration.

(a) Calculate the frequency of the light.

(b) Calculate the distance between two adjacent dark fringes on the screen.

Answer 1

(a) c = f λ … 3 x 10⁸ = f (550 x 10^–9) … f = 5.45 x 10¹⁴ Hz.

(b) m λ = d x₁ / L … (0.5) (550 x 10^–9) = (1.8 x 10^–5) x / 2.2 x 1= 0.0336 m first dark spot

m λ = d x₂ / L … (1.5) (550 x 10^–9) = (1.8x10^–5) x / 2.2 x2 = 0.101 m second dark spot

Distance between spots = .067 m

Alternatively you could find the location if the first bright spot from center and conclude the spacing of consecutive bright and dark spots are equal so should all be spaced by this amount.