Dependence of fringe width on lamda D and d
The fringe width in a double-slit interference pattern depends on three factors: the wavelength of the light (λ), the distance between the two slits (d), and the distance between the double-slit apparatus and the screen where the pattern is observed (D).
The formula for calculating the fringe width (Δy) is given by the equation:
Δy = (λ × D) / d
To understand the dependence of fringe width on λ, D, and d, let's break down the equation and see how each factor affects the fringe width:
1. Wavelength (λ): Fringe width is directly proportional to the wavelength of light. This means that as the wavelength increases, the fringe width also increases. This is because longer wavelengths result in wider interference fringes on the screen.
2. Distance between slits (d): Fringe width is inversely proportional to the distance between the two slits. As the distance between the slits increases, the fringe width decreases. This is because wider slit spacing results in narrower interference fringes.
3. Distance between double-slit and screen (D): Fringe width is directly proportional to the distance between the double-slit apparatus and the screen. As the distance increases, the fringe width also increases. This is because greater separation between the double slit and the screen leads to wider interference fringes.
In summary, the fringe width in a double-slit interference pattern depends on the wavelength of the light, the distance between the slits, and the distance between the double-slit apparatus and the screen. By understanding the relationship between these variables, you can calculate and manipulate the fringe width in interference patterns.