Interference, diffraction and spectra

A prism separates white light into colours, while a narrow slit produces bright and dark fringes where a ray picture predicts an even patch. Why are straight rays insufficient, and what can a pattern of colours tell us?

Recall adding displacements of two rope waves. For light, electric fields add at a point. With the same oscillation direction, matching phases strengthen the total oscillation and opposite phases weaken it; equal amplitudes can cancel to zero. This redistribution of intensity when waves overlap is interference. The rope analogy helps us add quantities, but in light it is a field that oscillates, not rope material.

Why do two ordinary torches not produce a steady fringe pattern? Their phases change rapidly and independently, so the eye sees an average. A stable pattern needs coherent waves: equal frequency and a maintained phase difference. Some places then stay reinforced and others weakened. Energy is not destroyed in a dark fringe: its flow is redistributed, strengthening neighbouring bright regions.

Make an opening narrower. Light beyond it does not simply form a narrower beam: it spreads more and enters the geometrical shadow. This is diffraction, wave behaviour at edges and openings that a straight-line model cannot capture. It is especially noticeable when size is comparable to wavelength. For sizes much greater than λ, angular spreading is usually small and rays become a good approximation again.

Replace one slit with many closely spaced identical slits: a diffraction grating. Their light reaches different points with different path differences. In some directions waves reinforce coherently; in others they weaken. Reinforcement directions depend on λ, so the components of complex light separate into a spectrum. Both diffraction and interference act here; no prism is needed.

A prism separates colours for another reason: ordinary glass has a frequency-dependent refractive index. This is dispersion. White light already contains different spectral components, and glass bends them differently. In an ordinary glass prism, violet bends more than red. Imagine the same index for all those frequencies: the beam would change direction, but this colour separation would disappear.

Relate two measures of monochromatic colour: in vacuum c = λν, with c ≈ 3·10⁸ м/с, λ in metres and ν in hertz. At constant c, halving λ doubles ν. Remember 1 нм = 10⁻⁹ м for optical wavelengths. In a medium, use its light speed v instead of c. Wavelength therefore changes on entering glass, although frequency stays the same at a stationary boundary.

A red object need not look red under every light. Under white light it mainly reflects red components and absorbs some others. If illumination contains almost none of the frequencies it reflects, it can look dark. Observed colour depends on source spectrum, surface properties and vision. A surface usually selects from incoming light, so 'red' does not promise that it emits red light itself.

Compare different sources' spectra. Hot dense matter usually produces a continuous spectrum with many neighbouring wavelengths. A dilute excited atomic gas emits distinct lines at particular frequencies. Their pattern is characteristic of the atoms and reveals composition. Lines raise a new question: why do atoms release energy only in such portions? We will soon return to atomic structure.

Pass continuous-spectrum light through a cooler dilute gas. Atoms absorb selected frequencies, leaving dark absorption lines on the background. The same atomic species has particular transitions in emission and absorption, so line positions identify the substance. This weakening comes from interaction with gas; it differs from a dark interference fringe, which needs no absorber.

Two waves in vacuum have wavelengths 400 and 800 nm. Which frequency is higher, and by what factor?

Both waves travel at c in vacuum, so ν = c/λ. The wavelength ratio already shows that 400 nm has twice the frequency of 800 nm.

For a numerical check, 400 нм = 4·10⁻⁷ м. Then ν₁ = 3·10⁸/(4·10⁻⁷) = 7,5·10¹⁴ Гц.

800 нм = 8·10⁻⁷ м, so ν₂ = 3,75·10¹⁴ Гц. The ratio is ν₁/ν₂ = 2.

Equal speed means equal λν products, not equal frequencies. A shorter wavelength is balanced by more frequent oscillations.

The 400 nm wave has twice the frequency: 7.5·10¹⁴ Hz versus 3.75·10¹⁴ Hz for 800 nm. Their vacuum speeds are equal.

Fields add during interference, so light can be strengthened or weakened without energy disappearing.

Narrow openings require waves; gratings and prisms separate spectra by different mechanisms.

The spectrum depends on source and matter along the light path; lines reveal atomic properties.

Visible light is only part of the electromagnetic spectrum.