The relationship between wavelength and angle of diffraction for a double slit can be described by the following equation:
sin(θ) = m * (λ / d),
where:
- θ is the angle of diffraction (measured from the original direction of the incident light to the direction of the diffracted light),
- m is the order of the interference fringe (an integer representing the number of dark and bright fringes),
- λ is the wavelength of the light, and
- d is the distance between the two slits (also known as the slit separation).
This equation is derived from the principles of wave interference and diffraction. When light passes through a double slit, it creates a pattern of constructive and destructive interference on a screen or detector placed behind the slits. The equation relates the angle at which these interference fringes occur (θ) to the wavelength of the light (λ), the distance between the slits (d), and the order of the fringe (m).
In this equation, the sine function captures the relationship between the angle of diffraction and the other variables. The variable m represents the order of the fringe, allowing for multiple sets of interference fringes to be observed. The wavelength of the light and the distance between the slits determine the spacing of the fringes.
In general, for a given double-slit setup, as the wavelength of the light decreases (shorter λ), the angle of diffraction (θ) increases. This means that the fringes become closer together and more tightly spaced. Conversely, if the wavelength increases (longer λ), the angle of diffraction decreases, resulting in wider-spaced fringes.
It's important to note that the equation assumes ideal conditions, such as a monochromatic light source, a parallel incident beam, and a perfect double-slit configuration. Real-world factors, such as the finite size of the slits, can introduce additional complexities to the diffraction pattern.