Calculate the Number of Dark Fringes on an Infinitely Large Screen

How many dark fringes will be produced on an infinitely large screen if orange light (λ = 590 nm) is incident on two slits that are 10.0 μm apart?

A. 305

Answer:

The number of total dark fringes produced on an infinitely large screen in this scenario is 305.

To determine the total number of dark fringes, we can calculate the angular separation of dark fringes using the formula for the angular position of dark fringes in a double-slit interference pattern: θ_dark = (m + 0.5) * (λ / d), where m is an integer, λ is the wavelength of light, and d is the distance between the slits.

Since the screen is infinitely large, the number of dark fringes will be determined by the maximum and minimum values of m for which the angle θ_dark is still within the range of 0 to 90 degrees.

By solving for the maximum integer value of m, we find that M is approximately 152.54. Rounding down to the nearest whole number, M = 152.

The total number of dark fringes is then twice the value of M plus 1 (to account for both sides of the central maximum), resulting in a total of 305 dark fringes on the screen.