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How does light's wave nature produce bright and dark fringes through slits and thin films?

Topic 14.7 Diffraction and Interference of Light: apply double-slit interference, diffraction gratings and thin-film interference using path difference.

A focused answer to AP Physics 2 Topics 14.7 to 14.9, covering diffraction, double-slit interference and the bright-fringe condition d sin theta = m lambda, diffraction gratings, thin-film interference, and how path difference produces constructive and destructive interference of light as evidence of its wave nature, with full worked examples.

Generated by Claude Opus 4.812 min answerUpdated 2026-06-04

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Quick answer

Light is a wave, so it diffracts (bends and spreads through openings or around edges) and interferes. In double-slit interference, light from two slits overlaps, and the path difference to a point decides the result: a whole number of wavelengths gives a bright fringe ( $d\sin\theta = m\lambda$ , constructive), and a half-odd number gives a dark fringe (destructive). The fringes spread wider for longer wavelength or smaller slit separation. A diffraction grating has many slits, giving sharp, bright maxima at the same angles, used to separate light into its colors. Thin-film interference (oil on water, soap bubbles) arises when light reflecting off the top and bottom of a thin film interferes by its path difference, producing colors. All of these patterns come from interference by path difference, the unmistakable signature that light is a wave.

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What this topic is asking
Diffraction: the bending of light
Double-slit interference and gratings
Thin-film interference
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What this topic is asking

The College Board (Topics 14.7 to 14.9) want you to apply diffraction, double-slit interference and thin-film interference to light, using path difference to find bright and dark fringes, as evidence of the wave nature of light.

Diffraction: the bending of light

Diffraction is the spreading of waves through gaps and around edges. Each point of a wavefront acts as a source of new wavelets, so light passing a narrow slit fans out rather than travelling straight, and these spread wavelets then interfere to make bright and dark bands. The effect is most pronounced when the opening is comparable to the wavelength. That light diffracts at all is proof of its wave nature, a stream of particles could not bend into a shadow.

Double-slit interference and gratings

The double-slit experiment is the classic demonstration of wave interference for light. Where the two paths differ by a whole wavelength, the waves arrive in phase and add (a bright fringe); where they differ by half a wavelength, they cancel (a dark fringe). The condition $d\sin\theta = m\lambda$ locates the bright fringes by order $m$ . Longer wavelengths and closer slits spread the fringes apart, which is why red light gives wider fringes than blue, and a fine grating, with thousands of slits, sharpens these into crisp spectral lines used to analyze light.

Thin-film interference

When light hits a thin film (a soap bubble, oil on water), part reflects off the top surface and part off the bottom. These two reflected waves have a path difference set by the film thickness, so they interfere, constructively for some wavelengths and destructively for others, producing the shifting colors seen in bubbles and oil slicks. The film thickness selects which colors reinforce, which is why the colors change with viewing angle and thickness. The strategic role of these physical-optics topics is that they are the decisive evidence that light is a wave: diffraction, double-slit fringes and thin-film colors all arise from interference by path difference, exactly the superposition idea of Topic 14.6 applied to light. This wave picture is complete and powerful, yet Unit 15 will show light also behaves as particles (photons), the wave-particle duality that the photoelectric effect reveals. Together, these topics frame the deepest question in modern physics: light is both wave and particle.

Wavelength from a double-slit pattern

In a double-slit experiment, the slits are $d = 5.0 \times 10^{-5}$ m apart. The first-order bright fringe ( $m = 1$ ) appears at an angle of $0.70$ degrees. Find the wavelength of the light.

step 1 Bright-fringe condition

$d\sin\theta = m\lambda$ , with $m = 1$ .

step 2 Solve for the wavelength

$\lambda = \dfrac{d\sin\theta}{m} = \dfrac{(5.0 \times 10^{-5})\sin 0.70^\circ}{1}$ .

step 3 Evaluate

$\sin 0.70^\circ = 0.0122$ , so $\lambda = (5.0 \times 10^{-5})(0.0122) = 6.1 \times 10^{-7}$ m.

step 4 Interpret

A wavelength of about $610$ nm is orange-red light. Measuring the fringe angle is a standard way to find an unknown wavelength, working only because light interferes as a wave.

Try this

Q1. State the condition (in terms of path difference) for a bright fringe in double-slit interference. [1 point]

Cue. The path difference is a whole number of wavelengths: $d\sin\theta = m\lambda$ .

Q2. State what diffraction and interference of light demonstrate about its nature. [1 point]

Cue. That light is a wave (particles would not spread or form interference fringes).

Exam-style practice questions

Practice questions written in the style of College Board exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

AP 2024 (style)7 marksSection II (long FRQ). Monochromatic light of wavelength

6.0 \times 10^{-7}

m passes through two slits separated by

d = 2.4 \times 10^{-5}

m. (a) Write the condition for a bright fringe in terms of the path difference. (b) Calculate the angle to the first-order (

m = 1

) bright fringe. (c) State and justify what happens to the fringe spacing if the slit separation is increased.

Show worked answer →

A 7-point FRQ on double-slit interference.

(a) Bright-fringe condition (2 points): a bright fringe occurs where the path difference is a whole number of wavelengths, $d\sin\theta = m\lambda$ for $m = 0, 1, 2, \dots$ (the waves arrive in phase).
(b) First-order angle (3 points): $\sin\theta = \dfrac{m\lambda}{d} = \dfrac{(1)(6.0 \times 10^{-7})}{2.4 \times 10^{-5}} = 0.025$ , so $\theta = \sin^{-1}(0.025) = 1.4$ degrees.
(c) Fringe spacing (2 points): a larger slit separation $d$ gives a smaller $\sin\theta$ for each order, so the fringes move closer together (the pattern shrinks).

Markers reward the path-difference condition, the first-order angle, and the inverse relation between slit separation and fringe spacing.

AP 2023 (style)1 marksSection I (multiple choice). Light passing through a single narrow slit spreads out and produces a pattern of bright and dark bands. This bending and spreading of waves is called (A) refraction (B) diffraction (C) polarization (D) reflection. Justify your reasoning.

Show worked answer →

A 1-point MCQ on diffraction. The answer is (B).

Diffraction is the bending and spreading of waves as they pass through an opening or around an edge; the resulting bright and dark bands come from interference of the spread wavelets. The trap is (A): refraction is bending at a boundary between media, not the spreading through a slit.

Related dot points

Sources & how we know this

AP Physics 2: Algebra-Based Course and Exam Description — College Board (2024)