Two Interference Patterns In a double-slit experiment the...

Two Interference Patterns In a double-slit experiment the distance between slits is $5.0 \mathrm{~nm}$ and the slits are $1.0 \mathrm{~m}$ from the screen. Two interference patterns can be seen on the screen: one due to light with wavelength $480 \mathrm{~nm}$, and the other due to light with wave length $600 \mathrm{~nm}$. What is the separation on the screen between the third-order $(m=3)$ bright fringes of the two interference patterns?

Key Concepts

Double-Slit Interference

Double-slit interference is a phenomenon where coherent light waves pass through two closely spaced slits, creating overlapping wavefronts that interfere with each other. This interference leads to the formation of a pattern of alternating bright (constructive interference) and dark (destructive interference) fringes on a screen, demonstrating the wave nature of light.

Interference Pattern

The interference pattern observed in a double-slit experiment consists of well-separated bright and dark regions on a screen. The pattern arises from the path difference between the light waves emanating from the two slits, where constructive interference occurs when this difference is an integer multiple of the wavelength and destructive interference occurs otherwise.

Fringe Spacing

Fringe spacing refers to the distance between adjacent bright (or dark) fringes on the interference pattern. It is directly related to the wavelength of the light, the distance from the slits to the screen, and the slit separation. The fringe spacing can be calculated using the formula ?y = (?L)/d, which shows that longer wavelengths yield wider separations and vice versa.

Order of Fringe

The order of a fringe, often denoted by m, indicates its position relative to the central maximum. The mth bright fringe corresponds to a situation where the path difference between the two slits is equal to m times the wavelength. This concept is key in analyzing which fringe (e.g., third-order, m = 3) is being considered in an interference pattern.

Please give Ace some feedback