What is b in single slit diffraction?
1 Answer
In single-slit diffraction, **\( b \)** represents the **width of the slit**, through which light (or other waveforms like sound or water waves) passes to create a diffraction pattern. This diffraction is the bending of waves around the edges of an obstacle or through an opening.
### Diffraction Pattern in a Single Slit
When monochromatic light passes through a single slit of width **\( b \)**, it spreads out and forms a series of bright and dark bands on a screen placed at a distance. This occurs due to the interference of the light waves emanating from different points across the slit. The main components of the pattern are:
- **Central maximum**: A bright spot at the center, which is the widest and most intense.
- **Secondary minima and maxima**: Alternating dark and bright spots forming at various angles from the center.
### Key Formulae Involving **\( b \)**
1. **Position of minima**: The positions of the dark fringes (minima) in the diffraction pattern occur where destructive interference happens. For the **n-th** minima, the condition is:
\[
b \sin(\theta_n) = n\lambda, \quad n = \pm 1, \pm 2, \pm 3, \dots
\]
Here:
- **\( \lambda \)** is the wavelength of the light passing through the slit.
- **\( \theta_n \)** is the angle of the n-th minima.
- **\( n \)** is an integer representing the order of the minima.
2. **Angular width of central maximum**: The angular width **\( \Delta \theta \)** of the central maximum (from the first minima on both sides) can be approximated by:
\[
\Delta \theta \approx \frac{2\lambda}{b}
\]
where **\( \lambda \)** is the wavelength of the light, and **\( b \)** is the width of the slit.
### Effect of Slit Width on Diffraction Pattern
- **As \( b \) increases**, the diffraction pattern narrows, and the central maximum becomes smaller, since less bending of the light occurs.
- **As \( b \) decreases**, the diffraction pattern spreads out, and the central maximum becomes wider.
In summary, **\( b \)** (slit width) plays a crucial role in determining the pattern's spacing and overall structure in single-slit diffraction.
### Diffraction Pattern in a Single Slit
When monochromatic light passes through a single slit of width **\( b \)**, it spreads out and forms a series of bright and dark bands on a screen placed at a distance. This occurs due to the interference of the light waves emanating from different points across the slit. The main components of the pattern are:
- **Central maximum**: A bright spot at the center, which is the widest and most intense.
- **Secondary minima and maxima**: Alternating dark and bright spots forming at various angles from the center.
### Key Formulae Involving **\( b \)**
1. **Position of minima**: The positions of the dark fringes (minima) in the diffraction pattern occur where destructive interference happens. For the **n-th** minima, the condition is:
\[
b \sin(\theta_n) = n\lambda, \quad n = \pm 1, \pm 2, \pm 3, \dots
\]
Here:
- **\( \lambda \)** is the wavelength of the light passing through the slit.
- **\( \theta_n \)** is the angle of the n-th minima.
- **\( n \)** is an integer representing the order of the minima.
2. **Angular width of central maximum**: The angular width **\( \Delta \theta \)** of the central maximum (from the first minima on both sides) can be approximated by:
\[
\Delta \theta \approx \frac{2\lambda}{b}
\]
where **\( \lambda \)** is the wavelength of the light, and **\( b \)** is the width of the slit.
### Effect of Slit Width on Diffraction Pattern
- **As \( b \) increases**, the diffraction pattern narrows, and the central maximum becomes smaller, since less bending of the light occurs.
- **As \( b \) decreases**, the diffraction pattern spreads out, and the central maximum becomes wider.
In summary, **\( b \)** (slit width) plays a crucial role in determining the pattern's spacing and overall structure in single-slit diffraction.