Can an object moving fast enough away from a stationary observer redshift out of the visible spectrum?

Question

I ran some numbers using the relativistic longitudinal Doppler effect formula $$\lambda_r = \sqrt{\frac{1+\beta}{1-\beta}}\cdot\lambda_s$$ where $\lambda_s$ and $\lambda_r$ are source and received wavelengths respectively, and $\beta = v/c$. Then I plugged in the wavelength of a red laser (630 nm) for $\lambda_s$ and solved for $v$, which gave me a result of $v=0.238c$ for the recieved wavelength to enter infrared territory, which doesn't seem that high (even though it's more than 20% lightspeed). So I would like to know if something like this has ever been observed or if it's even plausible.

Answer 1

Yes, of course. That is one of the main reasons that the James Webb Space Telescope focuses on the infrared part of the spectrum - galaxies at high redshift emit very little light in the visible part of the spectrum.

The redshift (in astronomy) $z$ is defined such that (in your terminology) $$\lambda_r = (1 + z) \lambda_s $$

Galaxies have been found with $z=10$ and upwards now, so for example, an emission line at 630 nm would be observed at 6.93 $\mu$m.