A source at rest emits light of wavelength 500 nm. When it is moving at 0.90c toward an observer, the observer detects light of wavelength:
A) 26 nm
B) 115 nm
C) 500 nm
D) 2200 nm
E) 9500 nm

Question

Quizplus · Accepted Answer

The observed wavelength is shorter due to the Doppler effect, as the source is moving towards the observer. The formula for relativistic Doppler shift is $\lambda' = \lambda \sqrt{\frac{1 - \beta}{1 + \beta}}$, where $\lambda'$ is the observed wavelength, $\lambda$ is the emitted wavelength, and $\beta = v/c$. Substituting $\lambda = 500$ nm and $\beta = 0.90$, we find $\lambda' \approx 115$ nm.

A Source at Rest Emits Light of Wavelength 500 Nm