Question

Two slits, each of width 1.8μm1.8μm and separated by the center-to-center distance of 3.6μmμm, are illuminated by plane waves from a krypton ion laser with a wavelength of 461.9 nm. a)What is the minimum slit width, in microns, for the entire pattern to contain 12 diffraction-pattern minima/zeros?

Answer 1

The minimum slit width for the entire diffraction pattern to contain 12 minima is 42.0 nm.

Step-by-step explanation:

To find the minimum slit width for the entire diffraction pattern to contain 12 minima, we can use the formula for the angular position of the mth minimum in a single-slit diffraction pattern:

sinθ = mλ / a

where θ is the angular position, λ is the wavelength, and a is the slit width.

In this case, we want to find the minimum slit width that results in 12 minima. The central maximum counts as the 0th minimum, so we need to have 11 minima on each side of the central maximum. Since the angular positions of the minima occur at increasing multiples of λ / a, we can set up the following equation:

11 * λ / a = π

Solving for a gives us the minimum slit width of a=πλ / 11 = (π * 461.9 nm) / 11 = 42.0 nm.