10.6.1. The single slit

In the discussion of Young’s experiment, we stated that a single narrow slit acts as a new source from which light spreads out. Even before Young, early experimenters – including Newton – had noticed that light spreads out from narrow holes and slits. It seems to turn around corners and enter regions where we would expect a shadow. These effects, known as diffraction, can only be properly understood using wave ideas. After all, you are hardly surprised to hear sound waves from someone talking around a corner!

A single slit can diffract light, which means it causes light waves to spread out as they pass through the slit. This behavior is observed even without knowledge of modern optics, as early scientists like Newton noted this effect. When light hits a narrow opening, it does not just travel in straight lines; instead, it spreads out and can even fill areas where you might expect to find a shadow, illustrating the wave-like nature of light.

Think of how sound travels. Just as you can hear someone speaking around a corner, light also spreads out when it passes through openings, creating patterns of light and dark, known as diffraction patterns.

When the double slit in Young’s experiment is replaced by a single narrow slit (illuminated by a monochromatic source), a broad pattern with a central bright region is seen. On both sides, there are alternate dark and bright regions, the intensity becoming weaker away from the centre (Fig. 10.15).

Replacing the double slit with a single slit produces a broad diffraction pattern. The center of this pattern is particularly bright, known as the central maximum, with alternating dark and bright bands, which occur due to the constructive and destructive interference of light waves spreading from different parts of the slit. As you move away from the center, the intensity of the bright regions decreases, illustrating how the wavefronts interfere.

Imagine a stone thrown into a pond. The ripples spread out from the point of impact in a circular pattern. In a similar way, when light passes through a slit, it creates waves that spread out instead of traveling straight ahead, leading to a pattern similar to those ripples.

The basic idea is to divide the slit into much smaller parts, and add their contributions at P with the proper phase differences. We are treating different parts of the wavefront at the slit as secondary sources. Because the incoming wavefront is parallel to the plane of the slit, these sources are in phase.

To analyze the light diffraction through a slit, we can imagine dividing the slit into many tiny segments that all act as individual sources of light waves. These sources emit light that can constructively or destructively interfere based on their relative phases when they meet at a point on a screen. Since the incoming waves are parallel, the phases of these secondary sources are synchronized, leading to clear patterns of light and dark bands.

Consider a choir singing. If everyone sings in unison (in phase), their voices combine to produce a powerful sound (constructive interference). If some members of the choir are slightly off-key or singing at different times (out of phase), the resulting sound is less intense or may even cancel out (destructive interference). Light behaves in a similar way as it passes through a slit.

It is observed that the intensity has a central maximum at q = 0 and other secondary maxima at q = (n+1/2)λ/a, which go on becoming weaker and weaker with increasing n. The minima (zero intensity) are at q = nλ/a, n = ±1, ±2, ±3, ....

The diffraction pattern exhibits a central bright maximum (the brightest spot) directly opposite the slit. As you move away from this center, there are areas of reduced and eventually zero intensity, known as minima, where the light waves completely cancel each other. The positions of the bright and dark spots can be mathematically described by specific formulas dependent on wavelength and slit width, reflecting how wave interference creates these patterns.

When you listen to music through a stereo system, colors of sound can be perceived more intensely at the center, while sounds may fade away towards the edges. Similarly, with light patterns from a slit, the brightest and darkest parts reflect how light interference varies with distance from the center.

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