3.2.2 Diffraction

Single-Slit Diffraction with Monochromatic Light

When monochromatic light (light of a single wavelength) passes through a narrow slit, it forms a diffraction pattern on a screen. The resulting pattern consists of a bright central fringe (twice the width of the other fringes) with alternating dark and bright fringes on either side.

• Central Bright Fringe: The most intense and broadest fringe in the pattern.
• Bright Fringes: Caused by constructive interference, where waves meet in phase.
• Dark Fringes: Caused by destructive interference, where waves are completely out of phase. The intensity of the fringes decreases with distance from the central fringe.

Diffraction of White Light

White light contains a range of wavelengths, each corresponding to a different colour. When white light passes through a slit:

• A central white maximum forms, surrounded by coloured fringes.
• The different wavelengths are diffracted by different amounts, creating a spectrum of colours.
• Violet (shorter wavelength) appears closer to the central maximum, while red (longer wavelength) is further away.

Factors Affecting Diffraction Patterns

1. Slit Width:

• Narrower Slit: Increases the amount of diffraction, causing the central maximum to be wider but with lower intensity.
• Wider Slit: Decreases diffraction, narrowing the central maximum and increasing its intensity.

2. Wavelength:

• Longer Wavelength: Increases diffraction, creating a wider central maximum with lower intensity.
• Shorter Wavelength: Reduces diffraction, producing a narrower central maximum with higher intensity.

Diffraction Gratings

A diffraction grating is an optical component with many closely spaced slits that diffract light. When monochromatic light passes through a diffraction grating, the interference pattern becomes sharper and brighter compared to that produced by a double-slit.

• Zero Order Line: The central bright fringe, aligned with the original light direction.
• First Order Lines: The first set of bright fringes on either side of the zero-order line.
• Higher Order Lines: Additional bright fringes further out, where the path difference equals multiples of the wavelength.

Diffraction Grating Formula:

$$d \sin \theta = n \lambda$$

where:

• $d$ is the distance between slits,
• $\theta$ is the angle from the normal to the maxima,
• $n$ is the order of the maximum,
• $\lambda$ is the wavelength of the light. This formula is derived from considering the path difference between adjacent rays of light that interfere constructively at each maximum.

Applications of Diffraction Gratings:

1. Astronomy: Diffraction gratings are used to analyse absorption spectra from stars, identifying the elements present.
2. X-ray Crystallography: X-rays, with wavelengths similar to atomic spacings, produce diffraction patterns when directed at crystals, allowing scientists to study atomic structures.