2aDiffraction
Discover how waves bend around obstacles and through openings, and apply single-slit and grating equations to predict diffraction patterns.
Diffraction reveals the wave nature of light and is the key principle behind spectroscopy, X-ray crystallography, and the colorful patterns on CDs — tools that underpin chemistry, biology, and materials science.
Lesson Overview
Diffraction is the bending and spreading of waves around obstacles or through openings. In this lesson you will explore single-slit diffraction, diffraction gratings, and the condition for minima. You will also see how diffraction is applied in X-ray crystallography and the colorful patterns on CDs.
Key Concepts
Diffraction
The bending and spreading of waves when they pass through a narrow opening or around an obstacle; most noticeable when the opening size is comparable to the wavelength.
Single-Slit Diffraction
A single slit of width a produces a central bright maximum flanked by dark minima. Minima occur at a sin θ = mλ (m = ±1, ±2, …).
Condition for Minima
a sin θ = mλ, where a is slit width, θ is the angle to the minimum, λ is wavelength, and m is a non-zero integer.
Diffraction Grating
Many equally spaced slits (spacing d); produces sharp, bright maxima at d sin θ = mλ. Used to separate wavelengths of light.
X-ray Crystallography
X-rays diffract off atomic planes in crystals; the pattern reveals atomic spacing and molecular structure (e.g., DNA double helix).
CDs and DVDs
The closely spaced tracks on a CD act as a diffraction grating, separating white light into a rainbow of colors.
Light of wavelength 600 nm passes through a single slit of width 0.10 mm. Find the angle of the first dark minimum.
A single slit of width 0.025 mm is illuminated with 500 nm light. Find the angle of the second dark minimum.
A diffraction grating has 500 lines/mm. Find the angle of the first-order maximum for 550 nm light.
Using the grating from Example 3, find the angle of the second-order maximum for 550 nm light.
A diffraction grating produces a first-order maximum at 20° for light of wavelength 480 nm. How many lines per mm does the grating have?
Light of wavelength 700 nm passes through a 0.050 mm slit. Find the angle of the first dark minimum.
Hint: Use a sin θ = mλ with m = 1. Convert all lengths to the same unit (meters) before dividing.
Why does diffraction become more noticeable as the slit width decreases?
Hint: Compare the ratio λ/a. What happens to sin θ (and therefore θ) as a gets smaller?
A diffraction grating has 300 lines/mm. What is the grating spacing d in meters?
Hint: d = 1/(lines per meter). Convert 300 lines/mm to lines/m first.
A grating with d = 1.5 × 10⁻⁶ m is illuminated with 600 nm light. Find the maximum order m that can be observed.
Hint: The maximum order occurs when sin θ = 1 (θ = 90°). Solve mλ/d ≤ 1 for m.
Explain why X-rays (λ ≈ 0.1 nm) rather than visible light are used to study crystal structure.
Hint: Compare the wavelength of X-rays to the spacing between atoms in a crystal (~0.1–0.3 nm).
Key Vocabulary
Diffraction
The bending and spreading of waves as they pass through an opening or around an obstacle; most pronounced when the opening is comparable in size to the wavelength.
Example: Sound diffracts around corners easily because its wavelength (cm to m) is comparable to everyday obstacles.
Single-Slit Diffraction
The diffraction pattern produced by a single narrow slit; characterized by a wide central maximum and narrower secondary maxima separated by dark minima at a sin θ = mλ.
Example: Shining a laser through a 0.1 mm slit produces a wide bright central band with dark fringes on either side.
Diffraction Grating
An optical element with many equally spaced slits or grooves; produces sharp, bright maxima at d sin θ = mλ and is used to separate (disperse) wavelengths.
Example: Spectroscopes use diffraction gratings to separate the colors in starlight and identify chemical elements.
Order (m)
An integer (0, ±1, ±2, …) labeling each bright maximum in a diffraction pattern; m = 0 is the central maximum.
Example: The first-order maximum (m = 1) appears at a smaller angle than the second-order maximum (m = 2).
Interactive Practice — 5 Questions
The condition for dark minima in single-slit diffraction is:
A diffraction grating with 400 lines/mm has grating spacing d equal to:
Diffraction is most noticeable when:
A grating (d = 2.0 × 10⁻⁶ m) gives a first-order maximum at 15° for a certain wavelength. What is λ?
X-ray crystallography works because:
Independent Practice
Light of wavelength 450 nm passes through a single slit of width 0.030 mm. Find the angles of the first and second dark minima.
A diffraction grating has 600 lines/mm. Find the angle of the first-order maximum for red light (λ = 700 nm) and violet light (λ = 400 nm).
Explain why a narrower slit produces a wider central diffraction maximum.
A CD has track spacing of about 1.6 μm. For what angle does first-order diffraction occur for green light (λ = 530 nm)?
★ A diffraction grating produces second-order maxima for two wavelengths at 30° and 45° respectively. Find both wavelengths if d = 2.4 × 10⁻⁶ m. Then find the angle separation between their third-order maxima.
ChallengeCommon Mistakes
Using the grating equation d sin θ = mλ for single-slit minima.
Single-slit minima use a sin θ = mλ (slit width a). The grating equation uses slit spacing d for maxima.
Forgetting to convert nm to meters before substituting into the diffraction equations.
Always convert: 1 nm = 1 × 10⁻⁹ m. Mixing nm and mm in the same equation gives wrong answers.
Thinking m = 0 gives a dark minimum in single-slit diffraction.
m = 0 is excluded from the minima condition; it corresponds to the bright central maximum.
Math Tips
For diffraction gratings, find d by taking the reciprocal of the line density: if the grating has N lines/mm, then d = 1/N mm. Convert to meters: d (m) = 1/(N × 10³).
The maximum possible order is m_max = floor(d/λ). Any m that gives sin θ > 1 is physically impossible — check this before reporting an answer.