Question

As an admirer of Thomas Young, you perform a double-slit experiment in his honor. You set your slits 1.01 mm apart and position your screen 3.65 m from the slits. Although Young had to struggle to achieve a monochromatic light beam of sufficient intensity, you simply turn on a laser with a wavelength of 641 nm . How far on the screen are the first bright fringe and the second dark fringe from the central bright fringe? Express your answers in millimeters.

Answer 1

Answer:

2.316e-3 and 3.47e-3

Explanation:

Now, at that angle, we look at the bright spots on the screen.

tan θ = x / L (x is the horizontal distance from the centre of the screen, L is distance to screen)

For small angles, we can approximate that tan θ = sin θ.

nλ / d = x / L         so then       x = n λ L / d

First bright fringe, n = 1

x = (1) (641*10^-9 m) (3.65 m) / (1.01*10^-3 m) = 2.316e-3

For destructive interference (dark fringes), equation becomes:

x = (n - 0.5) λ L / d

Second dark fringe, n = 1.5

x = 1.5 (641*10^-9 m) (3.65 m) / (1.01*10^-3 m) = 3.47e-3