What Diffraction Is
When light passes through a very narrow aperture or falls on an obstacle of very small dimensions, the law of rectilinear propagation is violated. At the edges, light bends into the region of the geometrical shadow. This bending of light around the edges of an obstacle is known as diffraction. If we look closely at the shadow cast by an opaque object, close to the region of geometrical shadow there are alternate dark and bright regions, just as in interference.
Diffraction is a general characteristic exhibited by all types of waves — sound waves, light waves, water waves or matter waves. Since the wavelength of light is much smaller than the dimensions of most obstacles, we do not encounter diffraction effects of light in everyday observation; light therefore appears to travel in straight lines. To observe diffraction the size of the aperture should be of the order of the wavelength of the incident wave, and the screen should be many times farther away than the aperture is wide.
Diffraction is based on the Huygens–Fresnel principle: each unobstructed point of a wavefront acts as a source of secondary wavelets, and the disturbance at any point beyond the aperture is the superposition of all these wavelets, added with the correct phase differences. The phenomenon defines the limit of ray optics — the ability of microscopes and telescopes to distinguish very close objects is set by the wavelength of light.
| Feature | Geometrical (ray) optics | Diffraction (wave) regime |
|---|---|---|
| Aperture size vs $\lambda$ | aperture $\gg \lambda$ | aperture $\sim \lambda$ |
| Edge of shadow | sharp | fringed, light enters shadow |
| Treatment of light | straight-line rays | superposition of wavelets |
| Everyday visibility | shadows, images | CD colours, streaks through eyelids |
The Single-Slit Geometry
Replace the double slit of Young's experiment by a single narrow slit of width $a$, 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, with the intensity becoming weaker away from the centre. Consider a parallel beam falling normally on the slit $LN$ of width $a$, with midpoint $M$. A line through $M$ perpendicular to the slit plane meets the screen at the centre $C$.
To find the intensity at a point $P$ on the screen, the lines joining $P$ to the different points $L, M, N$ of the slit are treated as parallel, making an angle $\theta$ with the normal $MC$. The slit is divided into many small parts, each treated as a secondary source. Because the incoming wavefront is parallel to the slit plane, these sources are all in phase as they leave the slit; the path difference between the wavelets from the two extreme edges, $L$ and $N$, is $a\sin\theta$.
Rays from the two edges of the slit reach $P$ with a path difference $a\sin\theta$. Pairing wavelets across the slit decides whether $P$ is dark or bright.
Condition for the Minima
At the centre $C$ ($\theta = 0$) every wavelet travels essentially the same path and they all arrive in phase, building a bright central maximum. Move off-axis to a point where the path difference between the two extreme edges is exactly $\lambda$, i.e. $a\sin\theta = \lambda$. Divide the slit into two halves: a wavelet from the top of the first half and the matching wavelet from the top of the second half are then $\lambda/2$ apart and cancel. Every such pair cancels, so the resultant intensity is zero. This gives the first minimum.
Repeating the pairing argument — dividing the slit into 4, 6, … equal strips — shows that the intensity vanishes whenever the extreme-edge path difference is an integral multiple of $\lambda$. The general condition for the minima (zero intensity) is therefore
$$a\sin\theta = n\lambda, \qquad n = \pm 1, \pm 2, \pm 3, \ldots$$The integer $n$ counts the order of the minimum. The value $n = 0$ is deliberately excluded — at $\theta = 0$ the whole wavefront adds constructively, giving the principal maximum rather than a dark band.
Single-slit minima vs YDSE maxima
The single-slit relation $a\sin\theta = n\lambda$ locates the minima of one slit of width $a$. The Young's double-slit relation $d\sin\theta = n\lambda$ locates the maxima for two slits separated by $d$. Same algebraic form, opposite meaning — and a different length symbol. Examiners flip the words "maxima" and "minima," or swap $a$ for $d$, to catch a hurried reader.
Diffraction: $a\sin\theta = n\lambda$ → dark. Interference (YDSE): $d\sin\theta = n\lambda$ → bright. Width $a$ ≠ separation $d$.
Secondary Maxima and Intensity
Between consecutive minima the cancellation is incomplete, leaving weaker bright bands called secondary maxima. Consider a direction where the extreme-edge path difference is $\tfrac{3}{2}\lambda$. Divide the slit into three equal strips: wavelets from two of the strips pair up with a $\lambda/2$ separation and cancel, but the third strip is left over and contributes constructively, producing brightness. Because only about one-third of the wavefront is left uncancelled, this maximum is far weaker than the central one.
The secondary maxima occur approximately where the path difference is a half-integral multiple of $\lambda$,
$$a\sin\theta \approx \left(n + \tfrac{1}{2}\right)\lambda, \qquad n = 1, 2, 3, \ldots$$and they become weaker and weaker as $n$ increases, since a smaller fraction of the wavefront survives the pairing. The central maximum at $\theta = 0$ is by far the brightest feature of the pattern.
The central maximum spans from $-\lambda/a$ to $+\lambda/a$; the secondary maxima between the outer minima are markedly fainter and confined to half that angular width.
The equally spaced bright fringes you must not confuse with this pattern come from Young's Double Slit Experiment.
Width of the Central Maximum
The central maximum is the bright band lying between the first minimum on one side and the first minimum on the other. Those first minima occur at $a\sin\theta = \pm\lambda$, i.e. $\sin\theta = \pm\lambda/a$. The full angular width of the central maximum is the angle between these two minima:
$$\Delta\theta = \frac{2\lambda}{a}$$Each secondary maximum, by contrast, spans only the gap between two adjacent higher-order minima — an angular spread of about $\lambda/a$. The central maximum is therefore twice as wide as the secondary maxima, and the NIOS text states this directly: the width of the central spot is twice the width of the other spots.
A single slit of width $a = 0.2\ \text{mm}$ is illuminated by light of wavelength $\lambda = 600\ \text{nm}$, with the pattern observed on a screen $D = 1.0\ \text{m}$ away. Find the linear width of the central maximum.
For small angles the half-angular width to the first minimum is $\theta_1 \approx \lambda/a$, so the linear half-width on the screen is $D\lambda/a$. The full width of the central maximum is
$$W = \frac{2D\lambda}{a} = \frac{2 \times 1.0 \times 600\times10^{-9}}{0.2\times10^{-3}} = 6.0\times10^{-3}\ \text{m} = 6.0\ \text{mm}.$$
Halving the slit width to $0.1\ \text{mm}$ would double this to $12\ \text{mm}$ — a narrower slit gives a wider pattern.
Narrower slit → wider pattern
Because the angular width $2\lambda/a$ is inversely proportional to $a$, shrinking the slit spreads the pattern out, while widening the slit squeezes it toward a sharp shadow. Students often expect a smaller slit to give a smaller pattern; the relationship is the reverse. Likewise, longer wavelength (red) diffracts more than shorter wavelength (blue), so red fringes are wider.
Smaller $a$ ⇒ larger $2\lambda/a$ ⇒ broader central band. Larger $\lambda$ ⇒ broader band.
Diffraction vs Interference
As Feynman noted, there is no sharp physical line between interference and diffraction — interference usually describes the superposition of a few sources, while diffraction describes the superposition from a continuous distribution of secondary sources across a wavefront. For NEET, the operational distinctions in the table below are what get tested. In the actual double-slit experiment, the screen pattern is a superposition of single-slit diffraction from each slit and the double-slit interference between them.
| Property | Single-slit diffraction | YDSE interference |
|---|---|---|
| Governing length | slit width $a$ | slit separation $d$ |
| Standard condition | a sinθ = nλ → minima | d sinθ = nλ → maxima |
| Fringe spacing | unequal; fall off from centre | equally spaced |
| Central band | twice as wide as side bands | same width as other fringes |
| Relative brightness | central maximum dominates | bright fringes nearly equal |
| Number of sources | continuous wavefront | two discrete coherent sources |
Diffraction and Resolution
Diffraction phenomena define the limits of ray optics. Because every aperture spreads light into a pattern of finite angular width, the images of two very close point objects are themselves small diffraction patches that overlap; beyond a point they can no longer be told apart. The limit of the ability of microscopes and telescopes to distinguish very close objects is therefore set by the wavelength of light — a smaller wavelength or a larger aperture improves the resolution.
A related idea is the distance over which a beam stays roughly collimated before diffraction widens it appreciably. A beam passing through an aperture of width $a$ spreads through an angle of order $\lambda/a$, so over a distance $z$ the spread is about $z\lambda/a$. This becomes comparable to $a$ itself at a characteristic length $z \approx a^2/\lambda$, the Fresnel distance, beyond which diffraction dominates and the ray description fails. In interference and diffraction light energy is only redistributed — darker regions lose what brighter regions gain — so energy is conserved throughout.
Diffraction of Light — at a glance
- Diffraction is the bending of light around edges; significant when aperture $\sim \lambda$.
- Single-slit minima: $a\sin\theta = n\lambda$, with $n = \pm1, \pm2, \ldots$ (never $n=0$).
- Secondary maxima: $a\sin\theta \approx (n+\tfrac{1}{2})\lambda$, growing weaker with $n$.
- Central maximum angular width $= 2\lambda/a$; it is twice as wide as the side bands.
- Narrower slit (smaller $a$) or longer $\lambda$ → wider pattern.
- Do not confuse with YDSE: $d\sin\theta = n\lambda$ gives equally spaced bright fringes.
- Diffraction sets the resolution limit of telescopes and microscopes.