# Doppler Effect for Light > Doppler effect for light in JEE Physics: Δλ/λ = v/c, relativistic formula, redshift and blueshift, Hubble expansion and the double-shift radar speed gun. - Canonical URL: https://prepelephant.com/topics/jee/physics/doppler-light-jee - Exam / course: JEE · Subject: Physics - Publisher: PrepElephant (https://prepelephant.com) — Prepared and reviewed by the PrepElephant Academic Review Team - First published: 2026-10-02 - Last updated: 2026-10-02 - How to cite: "Doppler Effect for Light", PrepElephant, https://prepelephant.com/topics/jee/physics/doppler-light-jee ## Direct answer Sound needs a medium, so its Doppler effect is asymmetric between source and observer; light needs none, so only relative motion counts and the formula is symmetric. For speeds much smaller than c, the fractional shift is Δλ/λ = Δν/ν = v/c: a source receding at speed v stretches every wavelength by the fraction v/c (redshift), an approaching one compresses it (blueshift). The exact relativistic expression for recession is ν' = ν√((1 − β)/(1 + β)) with β = v/c, which reduces to the linear law for β << 1. Astronomers define z = Δλ/λ₀ and use it as a speedometer — Hubble's law turns it into a distance ladder — and a radar speed gun exploits the double shift of a wave that travels out and back: Δν = 2v/λ. ## What you must remember - **Non-relativistic law:** Δλ/λ = Δν/ν = v/c; a galaxy receding at 0.1 per cent of c shifts every spectral line redward by 0.1 per cent. - **Sign convention:** receding → wavelength increases, frequency decreases (redshift); approaching → the opposite (blueshift); the colour words encode the whole logic. - **Relativistic exact form:** ν' = ν√((1 − β)/(1 + β)) for recession; use it whenever v is a sizable fraction of c, and check that β → 1 drives ν' → 0. - **Symmetry:** swapping "source moves" and "observer moves" changes nothing — no medium, no asymmetry; this is the sharpest contrast with sound. - **Astronomical redshift:** z = (λ_observed − λ₀)/λ₀ ≈ v/c; combined with Hubble's law (recession speed proportional to distance), z becomes a cosmic distance indicator. - **Radar double shift:** a wave reflected from a moving target is shifted twice, so the beat frequency against the transmitter is Δν = 2v/λ — the working principle of speed guns. - **Spectral-line fingerprint:** the shift is always measured against known laboratory lines (Hα at 656.3 nm, say), which is why the spectrometer is the Doppler instrument of astronomy. ## Redshift arithmetic A star's Hα line, laboratory value 656.3 nm, arrives at 656.7 nm. The shift is Δλ = 0.4 nm, so v = c(Δλ/λ) = 3 × 10⁸ × (0.4/656.3) ≈ 1.83 × 10⁵ m/s — about 183 km/s of recession, a typical value for a Milky Way star drifting relative to the Sun. Now the galaxy version: the same line appears at 721.9 nm, a 10 per cent redshift; at z = 0.1 the linear rule gives 0.1c as a first estimate, and the exact formula refines it to about 0.095c — the boundary where JEE stops and cosmology begins. The radar case closes the practical loop. A speed gun transmits at wavelength 3 cm (10 GHz); a car approaching at 30 m/s (108 km/h) returns a signal shifted twice: Δν = 2v/λ = 2 × 30/0.03 = 2000 Hz. The receiver beats echo against transmitter, and a countable 2 kHz audio tone stands in for highway speed. The factor of two is the trap and the teaching point: the car first meets more wavefronts as a moving observer, then re-emits the reflection as a moving source, and both shifts have the same sign. Weather radar and medical Doppler ultrasound run the identical arithmetic — one formula spanning traffic policing to blood-flow measurement. ## Light Doppler in exams The first separator from sound is symmetry: a question that distinguishes source-motion from observer-motion for light is testing whether you know no medium exists — for sound the two cases give different formulas, for light they cannot. Second, sign errors: receding means longer wavelength and lower frequency simultaneously, and options pair them correctly only in one row; reddening the frequency instead of the wavelength picks the mirrored wrong answer. Third, the radar factor of two is omitted in a classic distractor — the single-shift value sits among the options. Fourth, validity: the linear law needs v << c; a 0.8c problem requires the relativistic square-root form, and plugging 0.8 into v/c overestimates grossly. Main tests the fractional-shift plug-in and radar; Advanced has used Hubble-law combinations (distance from z via H₀ ≈ 70 km/s per megaparsec) and the distinction between Doppler, gravitational and expansion redshift in statement questions. ## Frequently asked questions ### How does the Doppler effect for light differ from that for sound? Light needs no medium, so only relative motion matters and source-versus-observer motion makes no difference; sound's two cases give different formulas because air anchors the asymmetry. ### What is the approximate Doppler shift formula for light? Δλ/λ = Δν/ν = v/c for speeds much smaller than c, with recession producing a longer wavelength (redshift) and approach a shorter one (blueshift). ### Why does a radar speed gun see a double Doppler shift? The moving vehicle acts first as a moving observer of the incoming wave and then as a moving source of the reflection, so the echo's frequency shifts by Δν = 2v/λ. ### How do astronomers measure a galaxy's recession speed? By comparing its spectral lines (like Hα at 656.3 nm) with laboratory wavelengths, converting the redshift z = Δλ/λ into speed through v ≈ zc, or the relativistic formula for large z. ### When must the relativistic Doppler formula be used? Whenever v is a significant fraction of c: ν' = ν√((1 − β)/(1 + β)) then replaces the linear approximation, which increasingly overestimates the shift as β grows.