What is the Intensity of Diffraction in a Single Slit?

The intensity of light observed in a diffraction pattern, specifically for a single slit, is not uniform but varies significantly with the angle from the central axis. This variation in intensity creates the characteristic pattern of bright and dark fringes.

The Intensity Equation

The distribution of light intensity in a single-slit diffraction pattern is described by a specific mathematical equation. According to the provided reference, the intensity ($I$) at a given point in the pattern is related to the maximum intensity ($I_{max}$) by the following formula:

$$I = I_{max} \frac{\sin^2 \phi}{\phi^2}$$

This equation shows how the intensity drops off as you move away from the center of the pattern.

Key Variables

To understand the intensity formula, it's important to define the variables involved:

• $I$: The intensity of light at a specific point in the diffraction pattern. This is what the equation calculates.
• $I_{max}$: The maximum intensity of light, which occurs at the very center of the diffraction pattern.
• $\phi$: A variable whose value depends on factors like the slit width, the wavelength of light, and the angle to the point of observation. Based on the provided reference, $\phi$ is defined as:
  • $\phi = (\pi a \sin 09-Jan-2020$
    (Note: The full physical meaning of this definition is unclear from the provided reference excerpt, as standard diffraction theory defines $\phi$ differently, typically relating to angle and wavelength).

Interpreting the Pattern

The equation $I = I_{max} \frac{\sin^2 \phi}{\phi^2}$ mathematically describes the visual pattern seen when light passes through a single slit:

• Central Maximum: When $\phi = 0$, the value $\frac{\sin^2 \phi}{\phi^2}$ approaches 1, resulting in $I = I_{max}$. This corresponds to the brightest point at the very center of the diffraction pattern.
• Minima (Dark Fringes): The intensity becomes zero ($I=0$) when $\sin \phi = 0$ (but $\phi \neq 0$). This occurs at specific values of $\phi$, corresponding to the dark regions or destructive interference in the pattern.
• Secondary Maxima (Bright Fringes): Between the minima, there are points of local maximum intensity. These secondary maxima are significantly less intense than the central maximum, and their intensity decreases as you move further away from the center.

In essence, the formula provides a quantitative way to predict the brightness of the light at any point in the single-slit diffraction pattern based on the variable $\phi$.