To solve the problem it is necessary to apply the concepts related to wavelength and error calculation.
The calculation of the error is usually defined by
[tex]z = \frac{\lambda_o-\lambda_r}{\lambda_r}[/tex]
Where
[tex]\lambda_o =[/tex] Wavelength from the observer
[tex]\lambda_r =[/tex] Wavelength from the rest
The previous formula is exactly equal to,
[tex]z= \frac{\lambda_o}{\lambda_r}-1[/tex]
[tex](z+1) = \frac{\lambda_o}{\lambda_r}[/tex]
[tex]\frac{\lambda_o}{\lambda_r}=(10+1)[/tex]
[tex]\lambda_o=11 \lambda_r[/tex]
Therefore the observed wavelength will be 11 times longer that the emitted wavelength.
If we make the comparison for the ultraviolet region (from 10nm to 400nm) we get that,
[tex]\lambda_o=11 \lambda_r[/tex]
[tex]\lambda_o=11 (\frac{10nm*400nm}}{2})[/tex]
[tex]\lambda_o = 2255nm[/tex]
That is the infrared region of electromagnetic spectra.
