Doppler effect for light (redshift and blueshift)

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The change in the **wavelength (and frequency)** of light you receive when its **source moves toward or away** from you.

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The observed wavelength is **stretched longer** (shifted toward red) because the source is **receding** (moving away).

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The observed wavelength is **squashed shorter** (shifted toward blue) because the source is **approaching** (moving toward you).

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$\dfrac{\Delta f}{f} = \dfrac{\Delta\lambda}{\lambda} \approx \dfrac{v}{c}$ — **given** in the data booklet (valid for v ≪ c).

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Rearrange to **v = (Δλ ÷ λ) × c**, where Δλ = observed − laboratory wavelength and c = 3.0 × 10⁸ m s⁻¹.

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The **change** in wavelength: observed wavelength − laboratory (true) wavelength — NOT the whole wavelength.

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**Red = Receding** (away, longer λ); **Blue = approaching** (toward, shorter λ).

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The **Universe is expanding**, so distant galaxies are **receding** from us — their light is shifted to longer (redder) wavelengths.

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The **approaching edge is blueshifted** (shorter λ) and the **receding edge is redshifted** (longer λ) at the same time.

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A **bigger** shift means a **faster** source — Δλ is proportional to v (Δλ/λ = v/c).

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Only when the source speed **v is much smaller than c** (the speed of light).

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Using the **whole observed wavelength** instead of the **change Δλ** (observed − lab) on the top of the fraction.

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Its spectral lines are at **different wavelengths** from the same lines in the lab: shifted to the red (moving away) or the blue (moving closer).

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Light needs **no medium**: only the relative speed of source and observer matters, and for v ≪ c the shift is Δλ/λ ≈ v/c.

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v = (Δλ/λ) c = 1.0 × 10⁻⁴ × 3.0 × 10⁸ = **3.0 × 10⁴ m s⁻¹, towards** us.