Diffraction

Diffraction is the spreading of light when it passes through a narrow opening or around an obstacle — a direct consequence of light's wave nature. Rather than continuing in a straight line, light waves passing through a slit fan out in various directions.

Key Takeaways

• Diffraction is the spreading of light through a narrow opening or around an obstacle, due to light's wave nature.

• Single-slit diffraction produces a fringe pattern with a central maximum; dark fringes occur at a sinθ = nλ (whole-integer order).

• Young's double-slit experiment produces interference from two overlapping wave sets: constructive interference (in-phase, bright maxima) and destructive interference (out-of-phase, dark minima).

• Double-slit dark fringes occur at d sinθ = (n + ½)λ (half-integer order) — distinct from the single-slit formula's whole-integer order.

• A diffraction grating uses many regularly spaced slits to separate wavelengths through interference, similar in effect to a prism's refraction-based dispersion.

Single-Slit Diffraction

Single-slit diffraction occurs when light passes through one narrow opening. Light waves diffract from the edges of the slit, and the effect is more pronounced when the slit width is on the same order of magnitude as the wavelength of light. As the slit narrows, the light spreads out even more widely.

When a lens focuses this diffracted light onto a screen, it produces a fringe pattern — alternating bright and dark bands. The central maximum, the brightest and widest band, sits at the center of the pattern. As the slit width shrinks, the central maximum widens and the spacing between fringes changes.

The angles at which dark fringes (destructive interference) appear are given by:

a sinθ = nλ

• a = width of the slit

• θ = angle from the center of the slit to a point of minimum intensity

• n = integer order of the dark fringe (1, 2, 3, ...)

• λ = wavelength of the incident light

Bright fringes appear in the gaps between these dark fringes.

Multiple Slits and Interference

With more than one slit, interference becomes the dominant effect: overlapping waves combine, either reinforcing or canceling each other.

In Young's double-slit experiment, light passes through two closely spaced slits, producing two overlapping sets of diffracted waves that interfere when they meet on a screen:

• Constructive interference: waves meeting in phase (peaks aligned) amplify each other, producing bright bands called maxima.

• Destructive interference: waves meeting out of phase (a peak aligned with a trough) cancel each other, producing dark bands called minima.

The angles of the dark fringes in a double-slit pattern depend on:

• d = distance between the two slits

• θ = angle of the dark fringe from the central axis

• n = integer fringe order

• λ = wavelength of light

MCAT Callout — Single-Slit vs. Double-Slit Dark Fringes: The formula for double-slit dark fringes uses a half-integer order term, since a dark fringe there requires a path-length difference of an odd multiple of a half-wavelength: d sinθ = (n + ½)λ. This looks similar to — but is not the same as — the single-slit dark-fringe formula above (a sinθ = nλ, whole-integer order). The double-slit bright-fringe (maxima) formula, by contrast, does use a whole-integer order term: d sinθ = nλ. Keeping straight which formula uses a whole integer and which uses a half-integer is a common MCAT trap.

Diffraction Gratings

A diffraction grating extends this idea by using many slits arranged in a regular, closely spaced pattern. When light passes through, each wavelength (color) of light interferes with itself and with the other wavelengths present, producing distinct, colorful patterns. This is similar in effect to how a prism disperses white light into colors — but where a prism separates colors through refraction, a diffraction grating separates them through interference.

Common MCAT Mistakes

• Mixing up the single-slit and double-slit dark-fringe formulas. Single-slit dark fringes use a whole-integer order (a sinθ = nλ); double-slit dark fringes use a half-integer order (d sinθ = (n + ½)λ). Swapping them is one of the most common diffraction errors on the exam.

• Assuming a narrower slit produces a narrower central maximum. The opposite is true — as slit width decreases, the central maximum widens and the fringe spacing changes.

• Confusing diffraction with refraction as the mechanism behind a diffraction grating's color separation. A diffraction grating separates wavelengths through interference, not refraction — that's what distinguishes it from a prism, which disperses color through refraction.

• Forgetting that constructive and destructive interference depend on phase, not just amplitude. Two waves meeting in phase (peaks aligned) reinforce each other regardless of their individual amplitudes; two waves meeting out of phase (peak against trough) cancel — the key variable is phase relationship, not wave strength alone.

MCAT-Style Concept Check

Question: Light of wavelength λ passes through a single slit of width a, producing a diffraction pattern on a screen. If the slit width a is decreased while the wavelength stays constant, what happens to the central maximum of the diffraction pattern?

• A) It narrows.

• B) It widens.

• C) It disappears entirely.

• D) It stays the same width.

Answer: B

Explanation: In single-slit diffraction, the dark fringes occur at angles given by a sinθ = nλ. As the slit width a decreases, the angle θ needed to satisfy this equation for the first dark fringe (n = 1) must increase — meaning the dark fringes move farther from the center, and the central maximum between them widens. This inverse relationship between slit width and diffraction spread is a hallmark of wave behavior: narrower openings produce more spreading.

FAQ

What causes diffraction?

Diffraction is caused by the wave nature of light. When light waves pass through a narrow opening or around an obstacle, they don't continue in a straight line — they spread out (fan out) in various directions, an effect that becomes more pronounced as the opening's width approaches the same order of magnitude as the light's wavelength.

What is the difference between diffraction and interference?

Diffraction is the spreading of light waves through a narrow opening or around an obstacle. Interference is what happens when two or more diffracted (or otherwise overlapping) waves combine — reinforcing each other where they meet in phase (constructive interference) or canceling where they meet out of phase (destructive interference). A double-slit experiment involves both: each slit diffracts the light, and the two diffracted wave sets then interfere.

Why does a diffraction grating produce sharper, more distinct bands than a double slit?

A diffraction grating uses many closely spaced slits instead of just two. Each additional slit adds another overlapping wave set to the interference pattern, which sharpens the bright bands (maxima) into narrower, more distinct lines compared to the broader maxima produced by only two slits.

How is a diffraction grating different from a prism?

Both separate white light into its component wavelengths (colors), but by different mechanisms. A prism disperses light through refraction — different wavelengths bend by different amounts passing through the prism material. A diffraction grating separates wavelengths through interference — each wavelength produces its own interference pattern at slightly different angles.