Single-Slit Diffraction
Understanding Single-Slit Diffraction
- When light passes through a single narrow slit, it spreads out and forms a diffraction pattern on a screen.
- This pattern consists of a central bright fringe flanked by dimmer and narrower fringes.
The central maximum is the brightest and widest part of the pattern, while the intensity of the fringes decreases as you move away from the center.
Mathematical Description of Diffraction
The position of the first minimum in the diffraction pattern is determined by the equation:
$$\theta = \frac{\lambda}{b}$$
where:
- $\theta$ is the angle of the first minimum
- $\lambda$ is the wavelength of the light
- $b$ is the width of the slit
This equation shows that the angle of the first minimum depends on the ratio of the wavelength to the slit width.Tip
Smaller slits or longer wavelengths result in wider diffraction patterns, while larger slits or shorter wavelengths produce narrower patterns.
Intensity Patterns
- The intensity of the diffraction pattern is highest at the central maximum and decreases for the secondary maxima.
- The first secondary maximum is about 4.5% as bright as the central maximum.
- If red light with a wavelength of $700 \, \text{nm}$ passes through a slit of width $1.4 \times 10^{-5} \, \text{m}$, the first minimum occurs at an angle of $0.05 \, \text{rad}$.
- This confirms the relationship $\theta = \frac{\lambda}{b}$.
Multiple Slits and Diffraction Gratings
Double-Slit Interference
- In a double-slit experiment, light passing through two slits creates an interference pattern of bright and dark fringes.
- The condition for constructive interference (bright fringes) is: $$d \sin \theta = n \lambda$$ where:
- $d$ is the distance between the slits
- $\theta$ is the angle of the fringe
- $n$ is the order of the fringe (an integer)
- $\lambda$ is the wavelength of the light
