Diffraction of Light

Wave phenomenon where light bends when passing through micro-sized slits or obstacles.

Conceptual context

When a beam of light passes through an extremely narrow slit, it does not merely cast a sharp geometric shadow on the screen behind it. Instead, the light bends laterally and spreads into the surrounding space, creating a pattern of bright and dark fringes on the screen. This remarkable wave phenomenon, in which light bends around obstacles and spreads when passing through micrometer-sized apertures, is known as the diffraction of light.

Diffraction through a single slit is a fundamental consequence of the wave nature of electromagnetic light. It connects geometric shadows with microscopic phase behavior. The central question guiding this leaf is: how do the aperture width and the wavelength influence the size and spread of the projected pattern? Its answer explains the resolution limits of microscopes, telescopes, and even the human eye.

[!NOTE] Diffraction occurs with all types of waves (sound, mechanical, electromagnetic). However, in the case of visible light, it is only noticeable to the naked eye if the obstacle or slit has microscopic dimensions comparable to its tiny wavelength.

🟢 Essential level

At a fundamental level, diffraction is explained by the wave principle that describes how every point on a propagating wavefront behaves as an individual source of small secondary spherical wavelets. When a light beam strikes a tiny slit, the aperture does not act simply as a geometric window; instead, the light passing through behaves as a coordinated assembly of countless tiny emitters aligned side-by-side.

As these secondary waves travel toward a distant screen, they cover slightly different distances depending on direction. At the center, all waves travel the same distance and arrive in phase, producing a bright central band.

Along specific inclined directions, however, waves from one half of the slit cancel corresponding waves from the other half. This produces a point of darkness known as the first diffraction minimum. The resulting pattern consists of a broad bright central band flanked by dark fringes and weaker secondary peaks.

[!TIP] If the slit is made narrower, the bright pattern on the screen spreads out significantly. This counterintuitive behavior is a hallmark of the wave nature of light.

🔵 Formal level

Basic formulas

The quantitative formulation of single-slit Fraunhofer diffraction is based on analyzing the optical path difference between secondary wavelets emerging from the aperture. The angle at which the destructive interference of all wavelets produces the first minimum of intensity is given by the fundamental relation:

Angle of the first diffraction minimum

In this expression, $\theta$ represents the angle of the first diffraction minimum, measured in radians relative to the central paraxial axis of incidence. The parameter $\lambda$ is the wavelength of light in meters, and $a$ is the physical width of the diffracting slit in meters.

When we project this angular pattern onto a flat observation screen placed at a longitudinal distance $L$, the lateral linear separation between the first upper minimum and the first lower minimum defines the total width of the bright central maximum. Under the paraxial approximation of small angles, where the tangent and the sine of the angle are approximately equal to the angle in radians, the linear width of the central maximum $w$ is calculated using the derived relation:

Width of the central maximum on the screen

Where $w$ is the width of the central maximum measured in meters on the screen, and $L$ is the distance from the slit to the screen in meters.

Real student questions

Why don't we see light diffraction in everyday life when walking through an open doorway? Doors and windows have widths on the order of meters, while visible wavelengths are microscopic. The angular deviation is therefore tiny, so light appears to travel geometrically straight. Sound diffracts much more through doors because its wavelengths are far larger.

What is the difference between diffraction and Young's double-slit interference? Diffraction is interference among continuous sources inside one slit. Young's pattern combines that single-slit diffraction with interference between two separated slits.

Does the first diffraction minimum represent actual darkness? Yes. In the ideal monochromatic model, phase cancellation is perfect along the first-minimum direction, so the intensity there is zero.

Final synthesis

Diffraction describes the lateral bending and angular spreading of light through a microscopic slit or obstacle. The key quantity is the ratio between $\lambda$ and $a$. In the paraxial Fraunhofer model, the first dark minimum angle $\theta$ is controlled by that ratio. On a screen at distance $L$, the central maximum width $w$ scales with $\lambda$ and $L$, and inversely with $a$. These relations allow optical calibration when the slit is much wider than the wavelength and the screen is far away.