Question

Relative to the central fringe, what is the position on a screen located 2.0 m away of the third order fringe in a double slit arrangement (d = 0.058 mm) when the slits are illuminated with λ = 480 m, light?

Answer 1

The position of the third order fringe in a double slit arrangement with a wavelength of 480 nm, a slit separation of 0.058 mm, and a screen distance of 2.0 m is approximately 4.97 cm from the central fringe.

Step-by-step explanation:

The question involves a double slit arrangement where the student is asked to determine the position of the third order fringe on a screen in a double-slit experiment. To calculate the position of the third order fringe, relative to the central fringe, we can use the formula for double-slit interference, which is:

y_n = (nλL) / d

Where:

• y_n is the distance from the central maximum to the nth order maximum on the screen.
• n is the order number of the fringe.
• λ is the wavelength of the light.
• L is the distance from the slits to the screen.
• d is the distance between the slits.

For the third order fringe (n = 3), the slit separation (d = 0.058 mm or 0.058×10⁻³ m), the distance to the screen (L = 2.0 m), and the wavelength of light (λ = 480 nm or 480×10⁻¹ m), we have:

y_3 = (3×480×10⁻¹ m×2.0 m) / (0.058×10⁻³ m) = 4.9655×10⁻² m

Thus, the position of the third order fringe is approximately 4.97 cm from the central fringe on the screen.